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1-stable fluctuation of the derivative martingale of branching random walk Stoch. Process. their Appl. (IF 1.4) Pub Date : 2024-03-13 Haojie Hou, Yan-Xia Ren, Renming Song
In this paper, we study the functional convergence in law of the fluctuations of the derivative martingale of branching random walk on the real line. Our main result strengthens the results of Buraczewski et al. (2021) and is the branching random walk counterpart of the main result of Maillard and Pain (2019) for branching Brownian motion.
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A detection problem with a monotone observation rate Stoch. Process. their Appl. (IF 1.4) Pub Date : 2024-03-12 Erik Ekström, Alessandro Milazzo
We study a quickest detection problem where the observation rate of the underlying process can be increased at any time for higher precision, but at an observation cost that grows linearly in the observation rate. This leads to a problem of , with a two-dimensional sufficient statistic comprised of the current observation rate together with the conditional probability that disorder has already happened
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A geometric extension of the Itô-Wentzell and Kunita’s formulas Stoch. Process. their Appl. (IF 1.4) Pub Date : 2024-03-11 Aythami Bethencourt de León, So Takao
We extend the Itô-Wentzell formula for the evolution along a continuous semimartingale of a time-dependent stochastic field driven by a continuous semimartingale to tensor field-valued stochastic processes on manifolds. More concretely, we investigate how the pull-back (respectively, the push-forward) by a stochastic flow of diffeomorphisms of a time-dependent stochastic tensor field driven by a continuous
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Heat kernel fluctuations and quantitative homogenization for the one-dimensional Bouchaud trap model Stoch. Process. their Appl. (IF 1.4) Pub Date : 2024-03-06 Sebastian Andres, David A. Croydon, Takashi Kumagai
We present on-diagonal heat kernel estimates and quantitative homogenization statements for the one-dimensional Bouchaud trap model. The heat kernel estimates are obtained using standard techniques, with key inputs coming from a careful analysis of the volume growth of the invariant measure of the process under study. As for the quantitative homogenization results, these include both quenched and annealed
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Wasserstein distance estimates for jump-diffusion processes Stoch. Process. their Appl. (IF 1.4) Pub Date : 2024-03-01 Jean-Christophe Breton, Nicolas Privault
We derive Wasserstein distance bounds between the probability distributions of a stochastic integral (Itô) process with jumps and a jump-diffusion process . Our bounds are expressed using the stochastic characteristics of and the jump-diffusion coefficients of evaluated in , and apply in particular to the case of different jump characteristics. Our approach uses stochastic calculus arguments and integrability
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The spatial sojourn time for the solution to the wave equation with moving time: Central and non-central limit theorems Stoch. Process. their Appl. (IF 1.4) Pub Date : 2024-02-29 Ciprian A. Tudor, Jérémy Zurcher
We consider the sojourn time of the solution to the stochastic wave equation with space–time white noise on the spatial domain . We analyze its asymptotic behavior in distribution when and the time variable also tends to infinity with , with . For , we prove that the properly renormalized sojourn time satisfies a Central Limit Theorem and we derive its rate of convergence under the Wasserstein distance
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Dependent conditional tail expectation for extreme levels Stoch. Process. their Appl. (IF 1.4) Pub Date : 2024-02-28 Yuri Goegebeur, Armelle Guillou, Jing Qin
We consider the estimation of the dependent conditional tail expectation, defined for a random vector with as , when , and where and denote the quantile functions of and , respectively. The distribution of is assumed to be of Pareto-type while the distribution of is kept general. Using extreme-value arguments we introduce an estimator for this risk measure for the situation , where is the number of
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The dual Derrida–Retaux conjecture Stoch. Process. their Appl. (IF 1.4) Pub Date : 2024-02-28 Xinxing Chen, Yueyun Hu, Zhan Shi
We consider a recursive system which was introduced by Collet et al. (1984)) as a spin glass model, and later by Derrida et al. (1992) and by Derrida and Retaux (2014) as a simplified hierarchical renormalization model. The system is expected to possess highly nontrivial universalities at or near criticality. In the nearly supercritical regime, Derrida and Retaux (2014) conjectured that the free energy
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A unified approach to the small-time behavior of the spectral heat content for isotropic Lévy processes Stoch. Process. their Appl. (IF 1.4) Pub Date : 2024-02-28 Kei Kobayashi, Hyunchul Park
This paper establishes the precise small-time asymptotic behavior of the spectral heat content for isotropic Lévy processes on bounded open sets of with , where the underlying characteristic exponents are regularly varying at infinity with index , including the case . Moreover, this asymptotic behavior is shown to be stable under an integrable perturbation of its Lévy measure. These results cover a
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Explosion and non-explosion for the continuous-time frog model Stoch. Process. their Appl. (IF 1.4) Pub Date : 2024-02-26 Viktor Bezborodov, Luca Di Persio, Peter Kuchling
We consider the continuous-time frog model on . At time , there are particles at , each of which is represented by a random variable. In particular, is a collection of independent random variables with a common distribution , , , . The particles at the origin are , all other ones being assumed as , or , hence not active. Active particles perform a simple symmetric continuous-time random walk in (that
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Diffusion dynamics for an infinite system of two-type spheres and the associated depletion effect Stoch. Process. their Appl. (IF 1.4) Pub Date : 2024-02-23 Myriam Fradon, Julian Kern, Sylvie Rœlly, Alexander Zass
We consider a random diffusion dynamics for an infinite system of hard spheres of two different sizes evolving in , its reversible probability measure, and its projection on the subset of the large spheres. The main feature is the occurrence of an attractive short-range dynamical interaction – known in the physics literature as a depletion interaction – between the large spheres, which is induced by
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Hyperbolic radial spanning tree Stoch. Process. their Appl. (IF 1.4) Pub Date : 2024-02-22 David Coupier, Lucas Flammant, Viet Chi Tran
We define and analyze an extension to the -dimensional hyperbolic space of the Radial Spanning Tree (RST) introduced by Baccelli and Bordenave in the two-dimensional Euclidean space (2007). In particular, we will focus on the description of the infinite branches of the tree. The properties of the two-dimensional Euclidean RST are extended to the hyperbolic case in every dimension: almost surely, every
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Fluctuations and moderate deviations for a catalytic Fleming–Viot branching system in nonequilibrium Stoch. Process. their Appl. (IF 1.4) Pub Date : 2024-02-22 Fuqing Gao, Yunshi Gao, Jie Xiong
We consider fluctuations and moderate deviations of the empirical fields for a catalytic Fleming–Viot branching system in nonequilibrium. We proved that for some independent initial distribution, the fluctuation process of the empirical fields is governed by an Ornstein–Uhlenbeck process whose drift term is a linear operator associated with a catalyst. Furthermore, we establish the large deviation
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Itô stochastic differentials Stoch. Process. their Appl. (IF 1.4) Pub Date : 2024-02-09 John Armstrong, Andrei Ionescu
We give an infinitesimal meaning to the symbol for a continuous semimartingale at an instant in time . We define a vector space structure on the space of differentials at time and deduce key properties consistent with the classical Itô integration theory. In particular, we link our notion of a differential with Itô integration via a stochastic version of the Fundamental Theorem of Calculus. Our differentials
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The importance Markov chain Stoch. Process. their Appl. (IF 1.4) Pub Date : 2024-02-08 Charly Andral, Randal Douc, Hugo Marival, Christian P. Robert
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Laplace principle for large population games with control interaction Stoch. Process. their Appl. (IF 1.4) Pub Date : 2024-02-06 Peng Luo, Ludovic Tangpi
This work investigates continuous time stochastic differential games with a large number of players whose costs and dynamics interact through the empirical distribution of both their states and their controls. The control processes are assumed to be open-loop. We give regularity conditions guaranteeing that if the finite-player game admits a Nash equilibrium, then both the sequence of equilibria and
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One-dimensional McKean–Vlasov stochastic variational inequalities and coupled BSDEs with locally Hölder noise coefficients Stoch. Process. their Appl. (IF 1.4) Pub Date : 2024-02-04 Ning Ning, Jing Wu, Jinwei Zheng
In this article, we investigate three classes of equations: the McKean–Vlasov stochastic differential equation (MVSDE), the MVSDE with a subdifferential operator referred to as the McKean–Vlasov stochastic variational inequality (MVSVI), and the coupled forward–backward MVSVI. The latter class encompasses the FBSDE with reflection in a convex domain as a special case. We establish the well-posedness
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On Rio’s proof of limit theorems for dependent random fields Stoch. Process. their Appl. (IF 1.4) Pub Date : 2024-02-02 Lê Vǎn Thành
This paper presents an exposition of Rio’s proof of the strong law of large numbers and extends his method to random fields. In addition to considering the rate of convergence in the Marcinkiewicz–Zygmund strong law of large numbers, we go a step further by establishing (i) the Hsu–Robbins–Erdös–Spitzer–Baum–Katz theorem, (ii) the Feller weak law of large numbers, and (iii) the Pyke–Root theorem on
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Wetting on a wall and wetting in a well: Overview of equilibrium properties Stoch. Process. their Appl. (IF 1.4) Pub Date : 2024-01-26 Quentin Berger, Brune Massoulié
We study the wetting model, which considers a random walk constrained to remain above a hard wall, but with additional pinning potential for each contact with the wall. This model is known to exhibit a wetting phase transition, from a localized phase (with trajectories pinned to the wall) to a delocalized phase (with unpinned trajectories). As a preamble, we take the opportunity to present an overview
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Infinitesimal gradient boosting Stoch. Process. their Appl. (IF 1.4) Pub Date : 2024-01-23 Clément Dombry, Jean-Jil Duchamps
We define infinitesimal gradient boosting as a limit of the popular tree-based gradient boosting algorithm from machine learning. The limit is considered in the vanishing-learning-rate asymptotic, that is when the learning rate tends to zero and the number of gradient trees is rescaled accordingly. For this purpose, we introduce a new class of randomized regression trees bridging totally randomized
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Green’s function for cut points of chordal SLE attached with boundary arcs Stoch. Process. their Appl. (IF 1.4) Pub Date : 2024-01-20 Dapeng Zhan
A technique of two-curve Green’s function is used to study the Green’s function of cut points of chordal SLEκ for κ∈(4,8). In order to apply the technique, we take the union of the SLE curve with two open boundary arcs, which share two boundary points other than the endpoints of the SLE curve. The Green’s function of interest is, for any z0 in the domain, the limit as r↓0 of the r−α times the probability
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Optimal estimation of the rough Hurst parameter in additive noise Stoch. Process. their Appl. (IF 1.4) Pub Date : 2024-01-19 Grégoire Szymanski
We estimate the Hurst parameter H∈(0,1) of a fractional Brownian motion from discrete noisy data, observed along a high-frequency sampling scheme. When the intensity τn of the noise is smaller in order than n−H we establish the LAN property with optimal rate n−1/2. Otherwise, we establish that the minimax rate of convergence is (n/τn2)−1/(4H+2) even when τn is of order 1. Our construction of an optimal
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The second class particle process at shocks Stoch. Process. their Appl. (IF 1.4) Pub Date : 2024-01-19 Patrik L. Ferrari, Peter Nejjar
We consider the totally asymmetric simple exclusion process (TASEP) starting with a shock discontinuity at the origin, with asymptotic densities λ to the left of the origin and ρ to the right of it and λ<ρ. We find an exact identity for the distribution of a second class particle starting at the origin. Then we determine the limiting joint distributions of the second class particle. Bypassing the last
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A series expansion formula of the scale matrix with applications in CUSUM analysis Stoch. Process. their Appl. (IF 1.4) Pub Date : 2024-01-14 Jevgenijs Ivanovs, Kazutoshi Yamazaki
We introduce a new Lévy fluctuation theoretic method to analyze the cumulative sum (CUSUM) procedure in sequential change-point detection. When observations are phase-type distributed and the post-change distribution is given by exponential tilting of its pre-change distribution, the first passage analysis of the CUSUM statistic is reduced to that of a certain Markov additive process. We develop a
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Large deviations for Markov processes with switching and homogenisation via Hamilton–Jacobi–Bellman equations Stoch. Process. their Appl. (IF 1.4) Pub Date : 2024-01-17 Serena Della Corte, Richard C. Kraaij
We consider the context of molecular motors modelled by a diffusion process driven by the gradient of a weakly periodic potential that depends on an internal degree of freedom. The switch of the internal state, that can freely be interpreted as a molecular switch, is modelled as a Markov jump process that depends on the location of the motor. Rescaling space and time, the limit of the trajectory of
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Lyapunov exponents in a slow environment Stoch. Process. their Appl. (IF 1.4) Pub Date : 2024-01-12 Tommaso Rosati
Motivated by the evolution of a population in a slowly varying random environment, we consider the 1D Anderson model on finite volume, with viscosity κ>0: (0.1)∂tu(t,x)=κΔu(t,x)+ξ(t,x)u(t,x),u(0,x)=u0(x),t>0,x∈T.The noise ξ is chosen constant on time intervals of length τ>0 and sampled independently after a time τ. We prove that the Lyapunov exponent λ(τ) is positive and near τ=0 follows a power law
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Asymptotic covariances for functionals of weakly stationary random fields Stoch. Process. their Appl. (IF 1.4) Pub Date : 2024-01-11 Leonardo Maini
Let (Ax)x∈Rd be a measurable, weakly stationary random field, i.e. E[Ax]=E[Ay], Cov(Ax,Ay)=K(x−y), ∀x,y∈Rd, with covariance function K:Rd→R. Assuming only that the integral covariance function wt≔∫{|z|≤t}K(z)dz is regularly varying (which encompasses the classical assumptions found in the literature), we compute limt→∞Cov∫tDAxdxtd/2wt1/2,∫tLAydytd/2wt1/2 for D,L⊆Rd belonging to a certain class of compact
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Measure-valued growth processes in continuous space and growth properties starting from an infinite interface Stoch. Process. their Appl. (IF 1.4) Pub Date : 2024-01-05 Apolline Louvet, Amandine Véber
The k-parent and infinite-parent spatial Lambda-Fleming Viot processes (or SLFV), introduced in Louvet (2023), form a family of stochastic models for spatially expanding populations. These processes are akin to a continuous-space version of the classical Eden growth model (but with local backtracking of the occupied area allowed when k is finite), while being associated with a dual process encoding
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Localization for constrained martingale problems and optimal conditions for uniqueness of reflecting diffusions in 2-dimensional domains Stoch. Process. their Appl. (IF 1.4) Pub Date : 2024-01-05 Cristina Costantini, Thomas G. Kurtz
We prove existence and uniqueness for semimartingale reflecting diffusions in 2-dimensional piecewise smooth domains with varying, oblique directions of reflection on each “side”, under geometric, easily verifiable conditions. Our conditions are optimal in the sense that, in the case of a convex polygon, they reduce to the conditions of Dai and Williams (1996), which are necessary for existence of
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Entropy and the discrete central limit theorem Stoch. Process. their Appl. (IF 1.4) Pub Date : 2024-01-04 Lampros Gavalakis, Ioannis Kontoyiannis
A strengthened version of the central limit theorem for discrete random variables is established, relying only on information-theoretic tools and elementary arguments. It is shown that the relative entropy between the standardised sum of n independent and identically distributed lattice random variables and an appropriately discretised Gaussian, vanishes as n→∞.
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Heat kernel bounds and Ricci curvature for Lipschitz manifolds Stoch. Process. their Appl. (IF 1.4) Pub Date : 2024-01-04 Mathias Braun, Chiara Rigoni
Given any d-dimensional Lipschitz Riemannian manifold (M,g) with heat kernel p, we establish uniform upper bounds on p which can always be decoupled in space and time. More precisely, we prove the existence of a constant C>0 and a bounded Lipschitz function R:M→(0,∞) such that for every x∈M and every t>0, supy∈Mp(t,x,y)≤Cmin{t,R2(x)}−d/2.This allows us to identify suitable weighted Lebesgue spaces
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A large deviation principle for the empirical measures of Metropolis–Hastings chains Stoch. Process. their Appl. (IF 1.4) Pub Date : 2024-01-03 Federica Milinanni, Pierre Nyquist
To sample from a given target distribution, Markov chain Monte Carlo (MCMC) sampling relies on constructing an ergodic Markov chain with the target distribution as its invariant measure. For any MCMC method, an important question is how to evaluate its efficiency. One approach is to consider the associated empirical measure and how fast it converges to the stationary distribution of the underlying
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Randomized empirical processes and confidence bands via virtual resampling Stoch. Process. their Appl. (IF 1.4) Pub Date : 2023-12-27 Miklós Csörgő
A data set of N labeled units, or labeled units of a finite population, may on occasions be viewed as if they were random samples {X1,…,XN}, N≥1, the first N of the labeled units from an infinite sequence X,X1,X2,… of independent real valued random variables with a common distribution function F. In case of such a view of a finite population, or when an accordingly viewed data set in hand is too big
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Long-range dependent completely correlated mixed fractional Brownian motion Stoch. Process. their Appl. (IF 1.4) Pub Date : 2023-12-20 Josephine Dufitinema, Foad Shokrollahi, Tommi Sottinen, Lauri Viitasaari
In this paper we introduce the long-range dependent completely correlated mixed fractional Brownian motion (ccmfBm). This is a process that is driven by a mixture of Brownian motion (Bm) and a long-range dependent completely correlated fractional Brownian motion (fBm, ccfBm) that is constructed from the Brownian motion via the Molchan–Golosov representation. Thus, there is a single Bm driving the mixed
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A stochastic target problem for branching diffusion processes Stoch. Process. their Appl. (IF 1.4) Pub Date : 2023-12-19 Idris Kharroubi, Antonio Ocello
We consider an optimal stochastic target problem for branching diffusion processes. This problem consists in finding the minimal condition for which a control allows the underlying branching process to reach a target set at a finite terminal time for each of its branches. This problem is motivated by an example from fintech where we look for the super-replication price of options on blockchain-based
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An explicit approximation for super-linear stochastic functional differential equations Stoch. Process. their Appl. (IF 1.4) Pub Date : 2023-12-16 Xiaoyue Li, Xuerong Mao, Guoting Song
Since it is difficult to implement implicit schemes on the infinite-dimensional space, we aim to develop the explicit numerical method for approximating super-linear stochastic functional differential equations (SFDEs). Precisely, borrowing the truncation idea and linear interpolation we propose an explicit truncated Euler–Maruyama (EM) scheme for SFDEs, and obtain the boundedness and convergence in
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Improved bounds for the total variation distance between stochastic polynomials Stoch. Process. their Appl. (IF 1.4) Pub Date : 2023-12-19 Egor Kosov, Anastasia Zhukova
The paper studies upper bounds for the total variation distance between the distributions of two polynomials of a special form in random vectors satisfying the Doeblin-type condition. Our approach is based on the recent results concerning the Nikolskii–Besov-type smoothness of the distribution densities of polynomials in logarithmically concave random vectors. The main results of the paper improve
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Two-dimensional random interlacements: 0-1 law and the vacant set at criticality Stoch. Process. their Appl. (IF 1.4) Pub Date : 2023-12-13 Orphée Collin, Serguei Popov
We correct and streamline the proof of the fact that, at the critical point α=1, the vacant set of the two-dimensional random interlacements is infinite (Comets and Popov, 2017). Also, we prove a zero–one law for a natural class of tail events related to the random interlacements.
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Approximate Message Passing for sparse matrices with application to the equilibria of large ecological Lotka–Volterra systems Stoch. Process. their Appl. (IF 1.4) Pub Date : 2023-12-17 Walid Hachem
This paper is divided into two parts. The first part is devoted to the study of a class of Approximate Message Passing (AMP) algorithms which are widely used in the fields of statistical physics, machine learning, or communication theory. The AMP algorithms studied in this part are those where the measurement matrix has independent elements, up to the symmetry constraint when this matrix is symmetric
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On the existence and uniqueness of solution to a stochastic Chemotaxis–Navier–Stokes model Stoch. Process. their Appl. (IF 1.4) Pub Date : 2023-12-15 Erika Hausenblas, Boris Jidjou Moghomye, Paul André Razafimandimby
In this article, we study a mathematical system modelling the dynamic of the collective behaviour of oxygen-driven swimming bacteria in an aquatic fluid flowing in a two dimensional bounded domain under stochastic perturbation. This model can be seen as a stochastic version of Chemotaxis–Navier–Stokes model. We prove the existence of a unique (probabilistic) strong solution. In addition, we establish
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Time-delayed generalized BSDEs Stoch. Process. their Appl. (IF 1.4) Pub Date : 2023-12-15 Luca Di Persio, Matteo Garbelli, Lucian Maticiuc, Adrian Zălinescu
We prove the existence and uniqueness of the solution of a BSDE with time-delayed generators in the small delay setting (or equivalently small Lipschitz constant), which employs the Stieltjes integral with respect to an increasing continuous stochastic process. Moreover, we obtain a result of continuity of the solution with regard to the increasing process, assuming only uniform convergence, but not
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No smooth phase transition for the nodal length of band-limited spherical random fields Stoch. Process. their Appl. (IF 1.4) Pub Date : 2023-12-09 Anna Paola Todino
In this paper, we investigate the variance of the nodal length for band-limited spherical random waves. When the frequency window includes a number of eigenfunctions that grows linearly, the variance of the nodal length is linear with respect to the frequency, while it is logarithmic when a single eigenfunction is considered. Then, it is natural to conjecture that there exists a smooth transition with
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Grid entropy in last passage percolation — A superadditive critical exponent approach Stoch. Process. their Appl. (IF 1.4) Pub Date : 2023-12-04 Alexandru Gatea
Working in the setting of i.i.d. last-passage percolation on RD with no assumptions on the underlying edge-weight distribution, we arrive at the notion of grid entropy — a Subadditive Ergodic Theorem limit of the entropies of paths with empirical measures weakly converging to a given target, or equivalently a deterministic critical exponent of canonical order statistics associated with the Levy-Prokhorov
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Limit of the environment viewed from Sinaï’s walk Stoch. Process. their Appl. (IF 1.4) Pub Date : 2023-11-30 Francis Comets, Oleg Loukianov, Dasha Loukianova
For Sinaï’s walk (Xk) we show that the empirical measure of the environment seen from the particle (ω̄k) converges in law to some random measure S∞. This limit measure is explicitly given in terms of the infinite valley, which construction goes back to Golosov (1984). As a consequence an “in law” ergodic theorem holds: 1n∑k=1nF(ω̄k)⟶ℒ∫ΩFdS∞.When the last limit is deterministic, it holds in probability
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Francis Comets’ Gumbel last passage percolation Stoch. Process. their Appl. (IF 1.4) Pub Date : 2023-12-01 Ivan Corwin
In 2015, Francis Comets shared with me a clever way to relate a model of directed last passage percolation with i.i.d. Gumbel edge weights to a special case of the log-gamma directed polymer model. To my knowledge, he never wrote this down. In the wake of his recent passing I am recording Francis’ observation along with some associated asymptotics and discussion. This note is dedicated in memory of
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Liouville theorem for V-harmonic maps under non-negative (m,V)-Ricci curvature for non-positive m Stoch. Process. their Appl. (IF 1.4) Pub Date : 2023-11-28 Kazuhiro Kuwae, Songzi Li, Xiang-Dong Li, Yohei Sakurai
Let V be a C1-vector field on an n-dimensional complete Riemannian manifold (M,g). We prove a Liouville theorem for V-harmonic maps satisfying various growth conditions from complete Riemannian manifolds with non-negative (m,V)-Ricci curvature for m∈[−∞,0]∪[n,+∞] into Cartan-Hadamard manifolds, which extends Cheng’s Liouville theorem proved in Cheng (1980) for sublinear growth harmonic maps from complete
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Asymptotic behavior of a class of multiple time scales stochastic kinetic equations Stoch. Process. their Appl. (IF 1.4) Pub Date : 2023-11-29 Charles-Edouard Bréhier, Shmuel Rakotonirina-Ricquebourg
We consider a class of stochastic kinetic equations, depending on two time scale separation parameters ɛ and δ: the evolution equation contains singular terms with respect to ɛ, and is driven by a fast ergodic process which evolves at the time scale t/δ2. We prove that when (ɛ,δ)→(0,0) the spatial density converges to the solution of a linear diffusion PDE. This result is a mixture of diffusion approximation
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Orthogonal intertwiners for infinite particle systems in the continuum Stoch. Process. their Appl. (IF 1.4) Pub Date : 2023-11-25 Stefan Wagner
This article focuses on a system of sticky Brownian motions, also known as Howitt–Warren martingale problem, and correlated Brownian motions and shows that infinite-dimensional orthogonal polynomials intertwine the dynamics of infinitely many particles and their n-particle evolution. The proof is based on two assumptions about the model: information about the reversible measures for the n-particle
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Approximate filtering via discrete dual processes Stoch. Process. their Appl. (IF 1.4) Pub Date : 2023-11-25 Guillaume Kon Kam King, Andrea Pandolfi, Marco Piretto, Matteo Ruggiero
We consider the task of filtering a dynamic parameter evolving as a diffusion process, given data collected at discrete times from a likelihood which is conjugate to the reversible law of the diffusion, when a generic dual process on a discrete state space is available. Recently, it was shown that duality with respect to a death-like process implies that the filtering distributions are finite mixtures
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The limit point in the Jante’s law process has an absolutely continuous distribution Stoch. Process. their Appl. (IF 1.4) Pub Date : 2023-11-20 Edward Crane, Stanislav Volkov
We study a stochastic model of consensus formation, introduced in 2015 by Grinfeld, Volkov and Wade, who called it a multidimensional randomized Keynesian beauty contest. The model was generalized by Kennerberg and Volkov, who called their generalization the Jante’s law process. We consider a version of the model where the space of possible opinions is a convex body B in Rd. N individuals in a population
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Regularity of the law of solutions to the stochastic heat equation with non-Lipschitz reaction term Stoch. Process. their Appl. (IF 1.4) Pub Date : 2023-11-20 Michael Salins, Samy Tindel
We prove the existence of a density for the solution to the multiplicative semilinear stochastic heat equation on an unbounded spatial domain, with drift term satisfying a half-Lipschitz type condition. The methodology is based on a careful analysis of differentiability for a map defined on weighted functional spaces.
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Spread of parasites affecting death and division rates in a cell population Stoch. Process. their Appl. (IF 1.4) Pub Date : 2023-11-17 Aline Marguet, Charline Smadi
We introduce a general class of branching Markov processes for the modelling of a parasite infection in a cell population. Each cell contains a quantity of parasites which evolves as a diffusion with positive jumps. The drift, diffusive function and positive jump rate of this quantity of parasites depend on its current value. The division rate of the cells also depends on the quantity of parasites
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Weak Dirichlet processes and generalized martingale problems Stoch. Process. their Appl. (IF 1.4) Pub Date : 2023-11-10 Elena Bandini, Francesco Russo
In this paper we explain how the notion of weak Dirichlet process is the suitable generalization of the one of semimartingale with jumps. For such a process we provide a unique decomposition: in particular we introduce characteristics for weak Dirichlet processes. We also introduce a weak concept (in law) of finite quadratic variation. We investigate a set of new useful chain rules and we discuss a
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Strong transience for one-dimensional Markov chains with asymptotically zero drifts Stoch. Process. their Appl. (IF 1.4) Pub Date : 2023-11-10 Chak Hei Lo, Mikhail V. Menshikov, Andrew R. Wade
For near-critical, transient Markov chains on the non-negative integers in the Lamperti regime, where the mean drift at x decays as 1/x as x→∞, we quantify degree of transience via existence of moments for conditional return times and for last exit times, assuming increments are uniformly bounded. Our proof uses a Doob h-transform, for the transient process conditioned to return, and we show that the
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Kernel representation formula: From complex to real Wiener–Itô integrals and vice versa Stoch. Process. their Appl. (IF 1.4) Pub Date : 2023-10-29 Huiping Chen, Yong Chen, Yong Liu
We characterize the relation between the real and complex Wiener–Itô integrals. Given a complex multiple Wiener–Itô integral, we get explicit expressions for the kernels of its real and imaginary parts. Conversely, considering a two-dimensional real Wiener–Itô integral, we obtain the representation formula by a finite sum of complex Wiener–Itô integrals. The main tools are a recursion technique and
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Nonparametric estimation for SDE with sparsely sampled paths: An FDA perspective Stoch. Process. their Appl. (IF 1.4) Pub Date : 2023-10-28 Neda Mohammadi, Leonardo V. Santoro, Victor M. Panaretos
We consider the problem of nonparametric estimation of the drift and diffusion coefficients of a Stochastic Differential Equation (SDE), based on n independent replicates Xi(t):t∈[0,1]1≤i≤n, observed sparsely and irregularly on the unit interval, and subject to additive noise corruption. By sparse we intend to mean that the number of measurements per path can be arbitrary (as small as two), and can
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The obstacle problem for stochastic porous media equations Stoch. Process. their Appl. (IF 1.4) Pub Date : 2023-10-20 Ruoyang Liu, Shanjian Tang
We study an obstacle problem for stochastic porous media equations, and show that it has a unique entropy solution with a method of penalty.
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Drift estimation for a multi-dimensional diffusion process using deep neural networks Stoch. Process. their Appl. (IF 1.4) Pub Date : 2023-10-20 Akihiro Oga, Yuta Koike
Recently, many studies have shed light on the high adaptivity of deep neural network methods in nonparametric regression models, and their superior performance has been established for various function classes. Motivated by this development, we study a deep neural network method to estimate the drift coefficient of a multi-dimensional diffusion process from discrete observations. We derive generalization
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Invariance of Brownian motion associated with exponential functionals Stoch. Process. their Appl. (IF 1.4) Pub Date : 2023-10-18 Yuu Hariya
It is well known that Brownian motion enjoys several distributional invariances such as the scaling property and the time reversal. In this paper, we prove another invariance of Brownian motion that is compatible with time reversal. The invariance, which seems to be new to our best knowledge, is described in terms of an anticipative path transformation involving exponential functionals as anticipating