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Onedimensional McKeanVlasov stochastic variational inequalities and coupled BSDEs with locally Hölder noise coefficients Stoch. Process. their Appl. (IF 1.4) Pub Date : 20240204
Ning Ning, Jing Wu, Jinwei ZhengIn this article, we investigate three classes of equations: the McKeanVlasov stochastic differential equation (MVSDE), the MVSDE with a subdifferential operator referred to as the McKeanVlasov 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 wellposedness

On Rio’s proof of limit theorems for dependent random fields Stoch. Process. their Appl. (IF 1.4) Pub Date : 20240202
Lê Vǎn ThànhThis 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

Wetting on a wall and wetting in a well: Overview of equilibrium properties Stoch. Process. their Appl. (IF 1.4) Pub Date : 20240126
Quentin Berger, Brune MassouliéWe 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

Infinitesimal gradient boosting Stoch. Process. their Appl. (IF 1.4) Pub Date : 20240123
Clément Dombry, JeanJil DuchampsWe define infinitesimal gradient boosting as a limit of the popular treebased gradient boosting algorithm from machine learning. The limit is considered in the vanishinglearningrate 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

Green’s function for cut points of chordal SLE attached with boundary arcs Stoch. Process. their Appl. (IF 1.4) Pub Date : 20240120
Dapeng ZhanA technique of twocurve 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

Optimal estimation of the rough Hurst parameter in additive noise Stoch. Process. their Appl. (IF 1.4) Pub Date : 20240119
Grégoire SzymanskiWe estimate the Hurst parameter H∈(0,1) of a fractional Brownian motion from discrete noisy data, observed along a highfrequency 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

The second class particle process at shocks Stoch. Process. their Appl. (IF 1.4) Pub Date : 20240119
Patrik L. Ferrari, Peter NejjarWe 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

A series expansion formula of the scale matrix with applications in CUSUM analysis Stoch. Process. their Appl. (IF 1.4) Pub Date : 20240114
Jevgenijs Ivanovs, Kazutoshi YamazakiWe introduce a new Lévy fluctuation theoretic method to analyze the cumulative sum (CUSUM) procedure in sequential changepoint detection. When observations are phasetype distributed and the postchange distribution is given by exponential tilting of its prechange distribution, the first passage analysis of the CUSUM statistic is reduced to that of a certain Markov additive process. We develop a

Large deviations for Markov processes with switching and homogenisation via Hamilton–Jacobi–Bellman equations Stoch. Process. their Appl. (IF 1.4) Pub Date : 20240117
Serena Della Corte, Richard C. KraaijWe 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

Lyapunov exponents in a slow environment Stoch. Process. their Appl. (IF 1.4) Pub Date : 20240112
Tommaso RosatiMotivated 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

Asymptotic covariances for functionals of weakly stationary random fields Stoch. Process. their Appl. (IF 1.4) Pub Date : 20240111
Leonardo MainiLet (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

Measurevalued growth processes in continuous space and growth properties starting from an infinite interface Stoch. Process. their Appl. (IF 1.4) Pub Date : 20240105
Apolline Louvet, Amandine VéberThe kparent and infiniteparent spatial LambdaFleming Viot processes (or SLFV), introduced in Louvet (2023), form a family of stochastic models for spatially expanding populations. These processes are akin to a continuousspace 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

Localization for constrained martingale problems and optimal conditions for uniqueness of reflecting diffusions in 2dimensional domains Stoch. Process. their Appl. (IF 1.4) Pub Date : 20240105
Cristina Costantini, Thomas G. KurtzWe prove existence and uniqueness for semimartingale reflecting diffusions in 2dimensional 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

Entropy and the discrete central limit theorem Stoch. Process. their Appl. (IF 1.4) Pub Date : 20240104
Lampros Gavalakis, Ioannis KontoyiannisA strengthened version of the central limit theorem for discrete random variables is established, relying only on informationtheoretic 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→∞.

Heat kernel bounds and Ricci curvature for Lipschitz manifolds Stoch. Process. their Appl. (IF 1.4) Pub Date : 20240104
Mathias Braun, Chiara RigoniGiven any ddimensional 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

A large deviation principle for the empirical measures of Metropolis–Hastings chains Stoch. Process. their Appl. (IF 1.4) Pub Date : 20240103
Federica Milinanni, Pierre NyquistTo 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

Randomized empirical processes and confidence bands via virtual resampling Stoch. Process. their Appl. (IF 1.4) Pub Date : 20231227
Miklós CsörgőA 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

Longrange dependent completely correlated mixed fractional Brownian motion Stoch. Process. their Appl. (IF 1.4) Pub Date : 20231220
Josephine Dufitinema, Foad Shokrollahi, Tommi Sottinen, Lauri ViitasaariIn this paper we introduce the longrange dependent completely correlated mixed fractional Brownian motion (ccmfBm). This is a process that is driven by a mixture of Brownian motion (Bm) and a longrange 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

A stochastic target problem for branching diffusion processes Stoch. Process. their Appl. (IF 1.4) Pub Date : 20231219
Idris Kharroubi, Antonio OcelloWe 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 superreplication price of options on blockchainbased

An explicit approximation for superlinear stochastic functional differential equations Stoch. Process. their Appl. (IF 1.4) Pub Date : 20231216
Xiaoyue Li, Xuerong Mao, Guoting SongSince it is difficult to implement implicit schemes on the infinitedimensional space, we aim to develop the explicit numerical method for approximating superlinear 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

Improved bounds for the total variation distance between stochastic polynomials Stoch. Process. their Appl. (IF 1.4) Pub Date : 20231219
Egor Kosov, Anastasia ZhukovaThe paper studies upper bounds for the total variation distance between the distributions of two polynomials of a special form in random vectors satisfying the Doeblintype condition. Our approach is based on the recent results concerning the Nikolskii–Besovtype smoothness of the distribution densities of polynomials in logarithmically concave random vectors. The main results of the paper improve

Twodimensional random interlacements: 01 law and the vacant set at criticality Stoch. Process. their Appl. (IF 1.4) Pub Date : 20231213
Orphée Collin, Serguei PopovWe correct and streamline the proof of the fact that, at the critical point α=1, the vacant set of the twodimensional 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.

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 : 20231217
Walid HachemThis 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

On the existence and uniqueness of solution to a stochastic Chemotaxis–Navier–Stokes model Stoch. Process. their Appl. (IF 1.4) Pub Date : 20231215
Erika Hausenblas, Boris Jidjou Moghomye, Paul André RazafimandimbyIn this article, we study a mathematical system modelling the dynamic of the collective behaviour of oxygendriven 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

Timedelayed generalized BSDEs Stoch. Process. their Appl. (IF 1.4) Pub Date : 20231215
Luca Di Persio, Matteo Garbelli, Lucian Maticiuc, Adrian ZălinescuWe prove the existence and uniqueness of the solution of a BSDE with timedelayed 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

No smooth phase transition for the nodal length of bandlimited spherical random fields Stoch. Process. their Appl. (IF 1.4) Pub Date : 20231209
Anna Paola TodinoIn this paper, we investigate the variance of the nodal length for bandlimited 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

Grid entropy in last passage percolation — A superadditive critical exponent approach Stoch. Process. their Appl. (IF 1.4) Pub Date : 20231204
Alexandru GateaWorking in the setting of i.i.d. lastpassage percolation on RD with no assumptions on the underlying edgeweight 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 LevyProkhorov

Limit of the environment viewed from Sinaï’s walk Stoch. Process. their Appl. (IF 1.4) Pub Date : 20231130
Francis Comets, Oleg Loukianov, Dasha LoukianovaFor 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

Francis Comets’ Gumbel last passage percolation Stoch. Process. their Appl. (IF 1.4) Pub Date : 20231201
Ivan CorwinIn 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 loggamma 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

Liouville theorem for Vharmonic maps under nonnegative (m,V)Ricci curvature for nonpositive m Stoch. Process. their Appl. (IF 1.4) Pub Date : 20231128
Kazuhiro Kuwae, Songzi Li, XiangDong Li, Yohei SakuraiLet V be a C1vector field on an ndimensional complete Riemannian manifold (M,g). We prove a Liouville theorem for Vharmonic maps satisfying various growth conditions from complete Riemannian manifolds with nonnegative (m,V)Ricci curvature for m∈[−∞,0]∪[n,+∞] into CartanHadamard manifolds, which extends Cheng’s Liouville theorem proved in Cheng (1980) for sublinear growth harmonic maps from complete

Asymptotic behavior of a class of multiple time scales stochastic kinetic equations Stoch. Process. their Appl. (IF 1.4) Pub Date : 20231129
CharlesEdouard Bréhier, Shmuel RakotonirinaRicquebourgWe 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

Orthogonal intertwiners for infinite particle systems in the continuum Stoch. Process. their Appl. (IF 1.4) Pub Date : 20231125
Stefan WagnerThis article focuses on a system of sticky Brownian motions, also known as Howitt–Warren martingale problem, and correlated Brownian motions and shows that infinitedimensional orthogonal polynomials intertwine the dynamics of infinitely many particles and their nparticle evolution. The proof is based on two assumptions about the model: information about the reversible measures for the nparticle

Approximate filtering via discrete dual processes Stoch. Process. their Appl. (IF 1.4) Pub Date : 20231125
Guillaume Kon Kam King, Andrea Pandolfi, Marco Piretto, Matteo RuggieroWe 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 deathlike process implies that the filtering distributions are finite mixtures

The limit point in the Jante’s law process has an absolutely continuous distribution Stoch. Process. their Appl. (IF 1.4) Pub Date : 20231120
Edward Crane, Stanislav VolkovWe 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

Regularity of the law of solutions to the stochastic heat equation with nonLipschitz reaction term Stoch. Process. their Appl. (IF 1.4) Pub Date : 20231120
Michael Salins, Samy TindelWe 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 halfLipschitz type condition. The methodology is based on a careful analysis of differentiability for a map defined on weighted functional spaces.

Spread of parasites affecting death and division rates in a cell population Stoch. Process. their Appl. (IF 1.4) Pub Date : 20231117
Aline Marguet, Charline SmadiWe 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

Weak Dirichlet processes and generalized martingale problems Stoch. Process. their Appl. (IF 1.4) Pub Date : 20231110
Elena Bandini, Francesco RussoIn 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

Strong transience for onedimensional Markov chains with asymptotically zero drifts Stoch. Process. their Appl. (IF 1.4) Pub Date : 20231110
Chak Hei Lo, Mikhail V. Menshikov, Andrew R. WadeFor nearcritical, transient Markov chains on the nonnegative 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 htransform, for the transient process conditioned to return, and we show that the

Kernel representation formula: From complex to real Wiener–Itô integrals and vice versa Stoch. Process. their Appl. (IF 1.4) Pub Date : 20231029
Huiping Chen, Yong Chen, Yong LiuWe 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 twodimensional 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

Nonparametric estimation for SDE with sparsely sampled paths: An FDA perspective Stoch. Process. their Appl. (IF 1.4) Pub Date : 20231028
Neda Mohammadi, Leonardo V. Santoro, Victor M. PanaretosWe 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

The obstacle problem for stochastic porous media equations Stoch. Process. their Appl. (IF 1.4) Pub Date : 20231020
Ruoyang Liu, Shanjian TangWe study an obstacle problem for stochastic porous media equations, and show that it has a unique entropy solution with a method of penalty.

Drift estimation for a multidimensional diffusion process using deep neural networks Stoch. Process. their Appl. (IF 1.4) Pub Date : 20231020
Akihiro Oga, Yuta KoikeRecently, 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 multidimensional diffusion process from discrete observations. We derive generalization

Invariance of Brownian motion associated with exponential functionals Stoch. Process. their Appl. (IF 1.4) Pub Date : 20231018
Yuu HariyaIt 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

Fluctuation analysis for particlebased stochastic reaction–diffusion models Stoch. Process. their Appl. (IF 1.4) Pub Date : 20231017
M. Heldman, S.A. Isaacson, J. Ma, K. SpiliopoulosRecent works have derived and proven the largepopulation meanfield limit for several classes of particlebased stochastic reaction–diffusion (PBSRD) models. These limits correspond to systems of partial integral–differential equations (PIDEs) that generalize standard massaction reaction–diffusion PDE models. In this work we derive and prove the next order fluctuation corrections to such limits,

Limit theorems for functionals of long memory linear processes with infinite variance Stoch. Process. their Appl. (IF 1.4) Pub Date : 20231014
Hui Liu, Yudan Xiong, Fangjun XuLet X={Xn:n∈N} be a long memory linear process in which the coefficients are regularly varying and innovations are independent and identically distributed and belong to the domain of attraction of an αstable law with α∈(0,2). Then, for any integrable and square integrable function K on R, under certain mild conditions, we establish the asymptotic behavior of the partial sum process ∑n=1[Nt][K(Xn)−EK(Xn)]:t≥0as

Scalefree percolation mixing time Stoch. Process. their Appl. (IF 1.4) Pub Date : 20231014
Alessandra Cipriani, Michele SalviAssign to each vertex of the onedimensional torus i.i.d. weights with a heavytail of index τ−1>0. Connect then each couple of vertices with probability roughly proportional to the product of their weights and that decays polynomially with exponent α>0 in their distance. The resulting graph is called scalefree percolation. The goal of this work is to study the mixing time of the simple random walk

Brownian motion can feel the shape of a drum Stoch. Process. their Appl. (IF 1.4) Pub Date : 20231014
Renan GrossWe study the scenery reconstruction problem on the ddimensional torus, proving that a criterion on Fourier coefficients obtained by Matzinger and Lember (2006) for discrete cycles applies also in continuous spaces. In particular, with the right drift, Brownian motion can be used to reconstruct any scenery. To this end, we prove an injectivity property of an infinite Vandermonde matrix.

Space–time boundedness and asymptotic behaviors of the densities of CMEsubordinators Stoch. Process. their Appl. (IF 1.4) Pub Date : 20231013
Masafumi Hayashi, Atsushi Takeuchi, Makoto YamazatoIn this article, we consider subordinators whose Lévy measures are represented as Laplace transforms of measures on (0,∞). We shall call them CMEsubordinators. Transition probabilities of such processes without drifts are absolutely continuous on (0,∞) with respect to Lebesgue measure on (0,∞). We show that the densities are space–time bounded on [t1,∞)×[x1,∞) for each t1>0 and x1>0, and the supremum

Elastic drifted Brownian motions and nonlocal boundary conditions Stoch. Process. their Appl. (IF 1.4) Pub Date : 20231005
Mirko D’Ovidio, Francesco IafrateWe provide a deep connection between elastic drifted Brownian motions and inverses to tempered subordinators. Based on this connection, we establish a link between multiplicative functionals and dynamical boundary conditions given in terms of nonlocal equations in time. Indeed, we show that the multiplicative functional associated to the elastic Brownian motion with drift is equivalent to a functional

Emergence of interlacements from the finite volume Bose soup Stoch. Process. their Appl. (IF 1.4) Pub Date : 20231004
Quirin VogelWe show that conditioned on the (empirical) particle density exceeding the critical value, the finite volume Bose loop soup converges to the superposition of the Bosonic loop soup (on the whole space) and the Poisson point process of random interlacements. The intensity of the latter is given by the excess density above the critical point. We consider both the free case and the meanfield case.

On eigenvalues of the Brownian sheet matrix Stoch. Process. their Appl. (IF 1.4) Pub Date : 20231001
Jian Song, Yimin Xiao, Wangjun YuanWe derive a system of stochastic partial differential equations satisfied by the eigenvalues of the symmetric matrix whose entries are the Brownian sheets. We prove that the sequence Ld(s,t),(s,t)∈[0,S]×[0,T]d∈N of empirical spectral measures of the rescaled matrices is tight on C([0,S]×[0,T],P(R)) and hence is convergent as d goes to infinity by Wigner’s semicircle law. We also obtain PDEs which are

Continuousstate branching processes with collisions: First passage times and duality Stoch. Process. their Appl. (IF 1.4) Pub Date : 20231001
Clément Foucart, Matija VidmarWe introduce a class of onedimensional positive Markov processes generalizing continuousstate branching processes (CBs), by taking into account a phenomenon of random collisions. Besides branching, characterized by a general mechanism Ψ, at a constant rate in time two particles are sampled uniformly in the population, collide and leave a mass of particles governed by a (sub)critical mechanism Σ.

Diffusion spiders: Green kernel, excessive functions and optimal stopping Stoch. Process. their Appl. (IF 1.4) Pub Date : 20230930
Jukka Lempa, Ernesto Mordecki, Paavo SalminenA diffusion spider is a strong Markov process with continuous paths taking values on a graph with one vertex and a finite number of edges (of infinite length). An example is Walsh’s Brownian spider where the process on each edge behaves as a Brownian motion. In this paper we calculate firstly the density of the resolvent kernel in terms of the characteristics of the underlying diffusion. Excessive

Central limit theorem in uniform metrics for generalized Kac equations Stoch. Process. their Appl. (IF 1.4) Pub Date : 20230929
Federico Bassetti, Lucia LadelliThe aim of this paper is to give explicit rates for the speed of convergence to equilibrium of the solution of the generalized Kac equation in two strong metrics: the total variation distance (TV) and the uniform metric between characteristic functions (χ0). A fundamental role in our study is played by the probabilistic representation of the solution of the generalized Kac equation as marginal law

On the meeting of random walks on random DFA Stoch. Process. their Appl. (IF 1.4) Pub Date : 20230928
Matteo Quattropani, Federico SauWe consider two random walks evolving synchronously on a random outregular graph of n vertices with bounded outdegree r≥2, also known as a random Deterministic Finite Automaton (DFA). We show that, with high probability with respect to the generation of the graph, the meeting time of the two walks is stochastically dominated by a geometric random variable of rate (1+o(1))n−1, uniformly over their

Diffusive fluctuations of longrange symmetric exclusion with a slow barrier Stoch. Process. their Appl. (IF 1.4) Pub Date : 20230927
Pedro Cardoso, Patrícia Gonçalves, Byron JiménezOviedoIn this article we obtain the equilibrium fluctuations of a symmetric exclusion process in Z with long jumps. The transition probability of the jump from x to y is proportional to x−y−γ−1. Here we restrict to the choice γ≥2 so that the system has a diffusive behaviour. Moreover, when particles move between negative integers sites and sites in N, the jump rates are slowed down by a factor αn−β, where

Large population limits of Markov processes on random networks Stoch. Process. their Appl. (IF 1.4) Pub Date : 20230920
Marvin Lücke, Jobst Heitzig, Péter Koltai, Nora Molkenthin, Stefanie WinkelmannWe consider timecontinuous Markovian discretestate dynamics on random networks of interacting agents and study the large population limit. The dynamics are projected onto lowdimensional collective variables given by the shares of each discrete state in the system, or in certain subsystems, and general conditions for the convergence of the collective variable dynamics to a meanfield ordinary differential

The stochastic balance equation for the American option value function and its gradient Stoch. Process. their Appl. (IF 1.4) Pub Date : 20230922
Malkhaz ShashiashviliIn the paper we consider the problem of valuation and hedging of American options written on dividendpaying assets whose price dynamics follow a multidimensional diffusion model. We derive a stochastic balance equation for the American option value function and its gradient. We prove that the latter pair is the unique solution of the stochastic balance equation as a result of the uniqueness in the

On a waitingtime result of Kontoyiannis: Mixing or decoupling? Stoch. Process. their Appl. (IF 1.4) Pub Date : 20230922
Giampaolo Cristadoro, Mirko Degli Esposti, Vojkan Jakšić, Renaud RaquépasWe introduce conditions of lower decoupling to the study of waitingtime estimations of the cross entropy between two mutually independent stationary stochastic processes. Although similar decoupling conditions have been used in the literature on large deviations and statistical mechanics, they appear largely unexplored in information theory. Building on a result of Kontoyiannis, namely Theorem 4 in

Local repulsion of planar Gaussian critical points Stoch. Process. their Appl. (IF 1.4) Pub Date : 20230920
Safa Ladgham, Raphaël LachiezeReyWe study the local repulsion between critical points of a stationary isotropic smooth planar Gaussian field. We show that the critical points can experience a soft repulsion which is maximal in the case of the random planar wave model, or a soft attraction of arbitrary high order. If the type of critical points is specified (extremum, saddle point), the points experience a hard local repulsion, that