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Probabilistic approach to singular perturbations of viscosity solutions to nonlinear parabolic PDEs Stoch. Process. their Appl. (IF 1.467) Pub Date : 20210721
Mingshang Hu, Falei WangIn this paper, we prove a convergence theorem for singular perturbations problems for a class of fully nonlinear parabolic partial differential equations (PDEs) with ergodic structures. The limit function is represented as the viscosity solution to a fully nonlinear degenerate PDEs. Our approach is mainly based on Gstochastic analysis argument. As a byproduct, we also establish the averaging principle

Moment bounds for dissipative semimartingales with heavy jumps Stoch. Process. their Appl. (IF 1.467) Pub Date : 20210729
Alexei Kulik, Ilya PavlyukevichIn this paper we show that if large jumps of an Itôsemimartingale X have a finite pmoment, p>0, the radial part of its drift is dominated by −Xκ for some κ≥−1, and the balance condition p+κ>1 holds true, then under some further natural technical assumptions one has supt≥0EXtpX<∞ for each pX∈(0,p+κ−1). The upper bound p+κ−1 is generically optimal. The proof is based on the extension of the method

Some properties of stationary continuous state branching processes Stoch. Process. their Appl. (IF 1.467) Pub Date : 20210729
Romain Abraham, JeanFrançois Delmas, Hui HeWe consider the genealogical tree of a stationary continuous state branching process with immigration. For a subcritical stable branching mechanism, we consider the genealogical tree of the extant population at some fixed time and prove that, up to a deterministic timechange, it is distributed as a continuoustime Galton–Watson process with immigration. We obtain similar results for a critical stable

Telegraph random evolutions on a circle Stoch. Process. their Appl. (IF 1.467) Pub Date : 20210715
Alessandro De Gregorio, Francesco IafrateWe consider the random evolution described by the motion of a particle moving on a circle alternating the angular velocities ±c and changing rotation at Poisson random times, resulting in a telegraph process over the circle. We study the analytic properties of the semigroup it generates as well as its probability distribution. The asymptotic behavior of the wrapped process is also discussed in terms

Discretetime simulation of Stochastic Volterra equations Stoch. Process. their Appl. (IF 1.467) Pub Date : 20210717
Alexandre Richard, Xiaolu Tan, Fan YangWe study discretetime simulation schemes for stochastic Volterra equations, namely the Euler and Milstein schemes, and the corresponding Multilevel MonteCarlo method. By using and adapting some results from Zhang (2008), together with the Garsia–Rodemich–Rumsey lemma, we obtain the convergence rates of the Euler scheme and Milstein scheme under the supremum norm. We then apply these schemes to approximate

A Yaglom type asymptotic result for subcritical branching Brownian motion with absorption Stoch. Process. their Appl. (IF 1.467) Pub Date : 20210728
Jiaqi LiuWe consider a slightly subcritical branching Brownian motion with absorption, where particles move as Brownian motions with drift −2+2ε, undergo dyadic fission at rate 1, and are killed when they reach the origin. We obtain a Yaglom type asymptotic result, showing that the long run expected number of particles conditioned on survival grows exponentially as 1∕ε as the process approaches criticality

Wong–Zakai approximations for quasilinear systems of Itô’s type stochastic differential equations Stoch. Process. their Appl. (IF 1.467) Pub Date : 20210722
Alberto Lanconelli, Ramiro ScorolliWe extend to the multidimensional case a Wong–Zakaitype theorem proved by Hu and Øksendal (1996) for scalar quasilinear Itô stochastic differential equations (SDEs). More precisely, with the aim of approximating the solution of a quasilinear system of Itô’s SDEs, we consider for any finite partition of the time interval [0,T] a system of differential equations, where the multidimensional Brownian

Rough nonlocal diffusions Stoch. Process. their Appl. (IF 1.467) Pub Date : 20210714
Michele Coghi, Torstein NilssenWe consider a nonlinear Fokker–Planck equation driven by a deterministic rough path which describes the conditional probability of a McKean–Vlasov diffusion with “common” noise. To study the equation we build a selfcontained framework of nonlinear rough integration theory which we use to study McKean–Vlasov equations perturbed by rough paths. We construct an appropriate notion of solution of the

Mean reflected stochastic differential equations with two constraints Stoch. Process. their Appl. (IF 1.467) Pub Date : 20210722
Adrian Falkowski, Leszek SłomińskiWe study the problem of the existence, uniqueness and stability of solutions of reflected stochastic differential equations (SDEs) with a minimality condition depending on the law of the solution (and not on the paths). We require that some functionals depending on the law of the solution lie between two given càdlàg constraints. Applications to investment models with constraints are given.

Mean field interaction on random graphs with dynamically changing multicolor edges Stoch. Process. their Appl. (IF 1.467) Pub Date : 20210721
Erhan Bayraktar, Ruoyu WuWe consider weakly interacting jump processes on timevarying random graphs with dynamically changing multicolor edges. The system consists of a large number of nodes in which the node dynamics depends on the joint empirical distribution of all the other nodes and the edges connected to it, while the edge dynamics depends only on the corresponding nodes it connects. Asymptotic results, including law

Irreducible decomposition for Markov processes Stoch. Process. their Appl. (IF 1.467) Pub Date : 20210707
Kazuhiro KuwaeWe prove an irreducible decomposition for Markov processes associated with quasiregular symmetric Dirichlet forms or local semiDirichlet forms under the absolute continuity condition of transition probability with respect to the underlying measure. We do not assume the conservativeness nor the existence of invariant measures for the processes. As applications, we establish a concrete expression for

Stochastic mSQG equations with multiplicative transport noises: White noise solutions and scaling limit Stoch. Process. their Appl. (IF 1.467) Pub Date : 20210704
Dejun Luo, Rongchan ZhuWe consider the modified Surface QuasiGeostrophic (mSQG) equation on the 2D torus T2, perturbed by multiplicative transport noise. The equation admits the white noise measure on T2 as the invariant measure. We first prove the existence of white noise solutions to the stochastic equation via the method of point vortex approximation, then, under a suitable scaling limit of the noise, we show that the

A hierarchical mean field model of interacting spins Stoch. Process. their Appl. (IF 1.467) Pub Date : 20210703
Paolo Dai Pra, Marco Formentin, Guglielmo PelinoWe consider a system of hierarchical interacting spins under dynamics of spinflip type with a ferromagnetic mean field interaction, scaling with the hierarchical distance, coupled with a system of linearly interacting hierarchical diffusions of Ornstein–Uhlenbeck type. In particular, the diffusive variables enter in the spinflip rates, effectively acting as dynamical magnetic fields. In absence of

Concentration on Poisson spaces via modified ΦSobolev inequalities Stoch. Process. their Appl. (IF 1.467) Pub Date : 20210625
Anna Gusakova, Holger Sambale, Christoph ThäleConcentration properties of functionals of general Poisson processes are studied. Using a modified ΦSobolev inequality a recursion scheme for moments is established, which is of independent interest. This is applied to derive moment and concentration inequalities for functionals on abstract Poisson spaces. Applications of the general results in stochastic geometry, namely Poisson cylinder models and

Brownian motion with a horizontal Bessel drift in a parabolictype domain Stoch. Process. their Appl. (IF 1.467) Pub Date : 20210622
Haneen Alayed, Dante DeBlassieWe extend the results of Lifshits and Shi for Brownian motion in parabolictype domains by including a Bessel drift in the horizontal direction.

Constructing fractional Gaussian fields from longrange divisible sandpiles on the torus Stoch. Process. their Appl. (IF 1.467) Pub Date : 20210624
Leandro Chiarini, Milton Jara, Wioletta M. RuszelIn Cipriani et al. (2017), the authors proved that, with the appropriate rescaling, the odometer of the (nearest neighbours) divisible sandpile on the unit torus converges to a biLaplacian field. Here, we study αlongrange divisible sandpiles, similar to those introduced in Frómeta and Jara (2018). We show that, for α∈(0,2), the limiting field is a fractional Gaussian field on the torus with parameter

An optimal stopping problem for spectrally negative Markov additive processes Stoch. Process. their Appl. (IF 1.467) Pub Date : 20210701
M. Çağlar, A. Kyprianou, C. VardarAcarPrevious authors have considered optimal stopping problems driven by the running maximum of a spectrally negative Lévy process as well as of a onedimensional diffusion; see e.g. Kyprianou and Ott (2014); Ott (2014); Ott (2013); Alvarez and Matomäki (2014); Guo and Shepp (2001); Pedersen (2000); Gapeev (2007). Many of the aforementioned results are either implicitly or explicitly dependent on Peskir’s

Continuity properties and the support of killed exponential functionals Stoch. Process. their Appl. (IF 1.467) Pub Date : 20210611
Anita Behme, Alexander Lindner, Jana Reker, Victor RiveroFor two independent Lévy processes ξ and η and an exponentially distributed random variable τ with parameter q>0, independent of ξ and η, the killed exponential functional is given by Vq,ξ,η≔∫0τe−ξs−dηs. Interpreting the case q=0 as τ=∞, the random variable Vq,ξ,η is a natural generalisation of the exponential functional ∫0∞e−ξs−dηs, the law of which is wellstudied in the literature as it is the stationary

Locally interacting diffusions as Markov random fields on path space Stoch. Process. their Appl. (IF 1.467) Pub Date : 20210621
Daniel Lacker, Kavita Ramanan, Ruoyu WuWe consider a countable system of interacting (possibly nonMarkovian) stochastic differential equations driven by independent Brownian motions and indexed by the vertices of a locally finite graph G=(V,E). The drift of the process at each vertex is influenced by the states of that vertex and its neighbors, and the diffusion coefficient depends on the state of only that vertex. Such processes arise

Moderate deviations of densitydependent Markov chains Stoch. Process. their Appl. (IF 1.467) Pub Date : 20210617
Xiaofeng XueA density dependent Markov chain (DDMC) introduced in Kurtz (1978) is a special continuous time Markov process. Examples are considered in fields like epidemics and processes which describe chemical reactions. Moreover the Yule process is a further example. In this paper we prove a moderate deviation principle for the paths of a certain class of DDMC. The proofs of the bounds utilize an exponential

Escape and absorption probabilities for Brownian motion in a quadrant Stoch. Process. their Appl. (IF 1.467) Pub Date : 20210617
Philip A. Ernst, Sandro Franceschi, Dongzhou HuangWe consider an obliquely reflected Brownian motion Z with positive drift in a quadrant stopped at time T, where T≔inf{t>0:Z(t)=(0,0)} is the first hitting time of the origin. Such a process can be defined even in the nonstandard case where the reflection matrix is not completelyS. We show that in this case the process has two possible behaviors: either it tends to infinity or it hits the corner (origin)

Formulae for the derivative of the Poincaré constant of Gibbs measures Stoch. Process. their Appl. (IF 1.467) Pub Date : 20210615
Julian SieberWe establish formulae for the derivative of the Poincaré constant of Gibbs measures on both compact domains and all of R d. As an application, we show that if the (not necessarily convex) Hamiltonian is an increasing function, then the Poincaré constant is strictly decreasing in the inverse temperature, and vice versa. Applying this result to the O(2) model allows us to give a sharpened upper bound

Regularity of multifractional moving average processes with random Hurst exponent Stoch. Process. their Appl. (IF 1.467) Pub Date : 20210608
Dennis Loboda, Fabian Mies, Ansgar StelandA recently proposed alternative to multifractional Brownian motion (mBm) with random Hurst exponent is studied, which we refer to as ItômBm. It is shown that ItômBm is locally selfsimilar. In contrast to mBm, its pathwise regularity is almost unaffected by the roughness of the functional Hurst parameter. The pathwise properties are established via a new polynomial moment condition similar to the

Estimates on transition densities of subordinators with jumping density decaying in mixed polynomial orders Stoch. Process. their Appl. (IF 1.467) Pub Date : 20210601
Soobin Cho, Panki KimIn this paper, we discuss estimates on the transition densities of subordinators, which are global in time. We establish sharp twosided estimates on the transition densities of subordinators whose Lévy measures are absolutely continuous and decaying in mixed polynomial orders. Under a weaker assumption on Lévy measures, we also obtain precise asymptotic behaviors of the transition densities at infinity

Twotype annihilating systems on complete and star graphs Stoch. Process. their Appl. (IF 1.467) Pub Date : 20210610
Irina Cristali, Yufeng Jiang, Matthew Junge, Remy Kassem, David Sivakoff, Grayson YorkRed and blue particles are placed in equal proportion throughout either the complete or star graph and iteratively sampled to take simple random walk steps. Mutual annihilation occurs when particles with different colors meet. We compare the time it takes to extinguish every particle to the analogous time in the (simple to analyze) onetype setting. Additionally, we study the effect of asymmetric particle

Diffusion approximations in the online increasing subsequence problem Stoch. Process. their Appl. (IF 1.467) Pub Date : 20210608
Alexander Gnedin, Amirlan SeksenbayevThe online increasing subsequence problem is a stochastic optimisation task with the objective to maximise the expected length of subsequence chosen from a random series by means of a nonanticipating decision strategy. We study the structure of optimal and nearoptimal subsequences in a standardised planar Poisson framework. Following a longstanding suggestion by Bruss and Delbaen (2004), we prove

Fiscal stimulus as an optimal control problem Stoch. Process. their Appl. (IF 1.467) Pub Date : 20210608
Philip A. Ernst, Michael B. Imerman, Larry Shepp, Quan ZhouDuring the Great Recession, Democrats in the United States argued that government spending could be utilized to “grease the wheels” of the economy in order to create wealth and to increase employment; Republicans, on the other hand, contended that government spending is wasteful and discouraged investment, thereby increasing unemployment. Today, in 2020, we find ourselves in the midst of another crisis

Fluctuation limits for meanfield interacting nonlinear Hawkes processes Stoch. Process. their Appl. (IF 1.467) Pub Date : 20210606
Sophie Heesen, Wilhelm StannatWe investigate the asymptotic behaviour of networks of interacting nonlinear Hawkes processes modeling a homogeneous population of neurons in the large population limit. In particular, we prove a functional central limit theorem for the mean spikeactivity thereby characterizing the asymptotic fluctuations in terms of a stochastic Volterra integral equation. Our approach differs from previous approaches

Detecting the presence of a random drift in Brownian motion Stoch. Process. their Appl. (IF 1.467) Pub Date : 20210606
P. Johnson, J.L. Pedersen, G. Peskir, C. ZuccaConsider a standard Brownian motion in one dimension, having either a zero drift, or a nonzero drift that is randomly distributed according to a known probability law. Following the motion in real time, the problem is to detect as soon as possible and with minimal probabilities of the wrong terminal decisions, whether a nonzero drift is present in the observed motion. We solve this problem for a

Lower Gaussian heat kernel bounds for the random conductance model in a degenerate ergodic environment Stoch. Process. their Appl. (IF 1.467) Pub Date : 20210521
Sebastian Andres, Noah HalberstamWe study the random conductance model on Zd with ergodic, unbounded conductances. We prove a Gaussian lower bound on the heat kernel given a polynomial moment condition and some additional assumptions on the correlations of the conductances. The proof is based on the wellestablished chaining technique. We also obtain bounds on the Green’s function.

Global solutions to stochastic wave equations with superlinear coefficients Stoch. Process. their Appl. (IF 1.467) Pub Date : 20210511
Annie Millet, Marta SanzSoléWe prove existence and uniqueness of a random field solution (u(t,x);(t,x)∈[0,T]×Rd) to a stochastic wave equation in dimensions d=1,2,3 with diffusion and drift coefficients of the form z(ln+(z))a for some a>0. The proof relies on a sharp analysis of moment estimates of time and space increments of the corresponding stochastic wave equation with globally Lipschitz coefficients. We give examples

On limit theorems for persistent Betti numbers from dependent data Stoch. Process. their Appl. (IF 1.467) Pub Date : 20210507
Johannes KrebsWe study persistent Betti numbers and persistence diagrams obtained from time series and random fields. It is well known that the persistent Betti function is an efficient descriptor of the topology of a point cloud. So far, convergence results for the (r,s)persistent Betti number of the qth homology group, βqr,s, were mainly considered for finitedimensional point cloud data obtained from i.i.d. observations

Extreme eigenvalues of nonlinear correlation matrices with applications to additive models Stoch. Process. their Appl. (IF 1.467) Pub Date : 20210517
Zijian Guo, CunHui ZhangThe maximum correlation of functions of a pair of random variables is an important measure of stochastic dependence. It is known that this maximum nonlinear correlation is identical to the absolute value of the Pearson correlation for a pair of Gaussian random variables or a pair of finite sums of iid random variables. This paper extends these results to pairwise Gaussian vectors and processes, nested

Large deviations in discretetime renewal theory Stoch. Process. their Appl. (IF 1.467) Pub Date : 20210513
Marco ZamparoWe establish sharp large deviation principles for cumulative rewards associated with a discretetime renewal model, supposing that each renewal involves a broadsense reward taking values in a real separable Banach space. The framework we consider is the pinning model of polymers, which amounts to a Gibbs change of measure of a classical renewal process and includes it as a special case. We first tackle

A critical branching process with immigration in random environment Stoch. Process. their Appl. (IF 1.467) Pub Date : 20210507
V.I. AfanasyevA Galton–Watson branching process with immigration evolving in a random environment is considered. Its associated random walk is assumed to be oscillating. We prove a functional limit theorem in which the process under consideration is normalized by a random coefficient depending on the random environment only. The distribution of the limiting process is described in terms of a strictly stable Levy

Timeinhomogeneous Gaussian stochastic volatility models: Large deviations and super roughness Stoch. Process. their Appl. (IF 1.467) Pub Date : 20210504
Archil GulisashviliWe introduce timeinhomogeneous stochastic volatility models, in which the volatility is described by a nonnegative function of a Volterra type continuous Gaussian process that may have very rough sample paths. The main results obtained in the paper are sample path and smallnoise large deviation principles for the logprice process in a timeinhomogeneous super rough Gaussian model under very mild

Averaging principle for stochastic differential equations in the random periodic regime Stoch. Process. their Appl. (IF 1.467) Pub Date : 20210510
Kenneth UdaWe present the validity of stochastic averaging principle for nonautonomous slow–fast stochastic differential equations (SDEs) whose fast motions admit random periodic solutions. Our investigation is motivated by some problems arising from multiscale stochastic dynamical systems, where configurations are time dependent due to nonlinearity of the underlying vector fields and the onset of time dependent

Joint Hölder continuity of local time for a class of interacting branching measurevalued diffusions Stoch. Process. their Appl. (IF 1.467) Pub Date : 20210504
D.A. Dawson, J. Vaillancourt, H. WangUsing a Tanaka representation of the local time for a class of superprocesses with dependent spatial motion, as well as sharp estimates from the theory of uniformly parabolic partial differential equations, the joint Hölder continuity in time and space of said local times is obtained in two and three dimensional Euclidean space.

On estimation of quadratic variation for multivariate pure jump semimartingales Stoch. Process. their Appl. (IF 1.467) Pub Date : 20210507
Johannes Heiny, Mark PodolskijIn this paper we present the asymptotic analysis of the realised quadratic variation for multivariate symmetric βstable Lévy processes, β∈(0,2), and certain pure jump semimartingales. The main focus is on derivation of functional limit theorems for the realised quadratic variation and its spectrum. We will show that the limiting process is a matrixvalued βstable Lévy process when the original process

Asymptotic behavior for Markovian iterated function systems Stoch. Process. their Appl. (IF 1.467) Pub Date : 20210428
ChengDer FuhLet (U,d) be a complete separable metric space and (Fn)n≥0 a sequence of random functions from U to U. Motivated by studying the stability property for Markovian dynamic models, in this paper, we assume that the random function (Fn)n≥0 is driven by a Markov chain X={Xn,n≥0}. Under some regularity conditions on the driving Markov chain and the mean contraction assumption, we show that the forward iterations

On excursions inside an excursion Stoch. Process. their Appl. (IF 1.467) Pub Date : 20210428
MayRu Chen, JuYi YenThe distribution of ranked heights of excursions of a Brownian bridge is given by Pitman and Yor (2001). In this work, we consider excursions of a Brownian excursion above a random level x, where x is the value of the excursion at an independent uniform time on [0,1]. We study the maximum heights of these excursions as Pitman and Yor did for excursions of a Brownian bridge. In particular, the probability

Limit theorems for cloning algorithms Stoch. Process. their Appl. (IF 1.467) Pub Date : 20210422
Letizia Angeli, Stefan Grosskinsky, Adam M. JohansenLarge deviations for additive path functionals of stochastic processes have attracted significant research interest, in particular in the context of stochastic particle systems and statistical physics. Efficient numerical ‘cloning’ algorithms have been developed to estimate the scaled cumulant generating function, based on importance sampling via cloning of rare event trajectories. So far, attempts

Optimal stationary markings Stoch. Process. their Appl. (IF 1.467) Pub Date : 20210420
Bartłomiej Błaszczyszyn, Christian HirschMany specific problems ranging from theoretical probability to applications in statistical physics, combinatorial optimization and communications can be formulated as an optimal tuning of local parameters in large systems of interacting particles. Using the framework of stationary point processes in the Euclidean space, we pose it as a problem of an optimal stationary marking of a given stationary

Limit theorems for topological invariants of the dynamic multiparameter simplicial complex Stoch. Process. their Appl. (IF 1.467) Pub Date : 20210422
Takashi Owada, Gennady Samorodnitsky, Gugan ThoppeThe topological study of existing random simplicial complexes is nontrivial and has led to several seminal works. However, the applicability of such studies is limited since a single parameter usually governs the randomness in these models. With this in mind, we focus here on the topology of the recently proposed multiparameter random simplicial complex. In particular, we introduce a dynamic variant

The 1/estrategy is suboptimal for the problem of best choice under no information Stoch. Process. their Appl. (IF 1.467) Pub Date : 20210430
F. Thomas Bruss, L.C.G. RogersThis paper answers a longstanding open question concerning the 1∕estrategy for the problem of best choice. N candidates for a job arrive at times independently uniformly distributed in [0,1]. The interviewer knows how each candidate ranks relative to all others seen so far, and must immediately appoint or reject each candidate as they arrive. The aim is to choose the best overall. The 1∕e strategy

Exponential mixing under controllability conditions for sdes driven by a degenerate Poisson noise Stoch. Process. their Appl. (IF 1.467) Pub Date : 20210415
Vahagn Nersesyan, Renaud RaquépasWe prove existence and uniqueness of the invariant measure and exponential mixing in the totalvariation norm for a class of stochastic differential equations driven by degenerate compound Poisson processes. In addition to mild assumptions on the distribution of the jumps for the driving process, the hypotheses for our main result are that the corresponding control system is dissipative, approximately

On stochastic Itô processes with drift in Ld Stoch. Process. their Appl. (IF 1.467) Pub Date : 20210418
N.V. KrylovFor Itô stochastic processes in Rd with drift in Ld Aleksandrov’s type estimates are established in the elliptic and parabolic settings. They are applied to estimating the resolvent operators of the corresponding elliptic and parabolic operators in Lp and Lp+1, respectively, where p≥d.

Markov chains in random environment with applications in queueing theory and machine learning Stoch. Process. their Appl. (IF 1.467) Pub Date : 20210420
Attila Lovas, Miklós RásonyiWe prove the existence of limiting distributions for a large class of Markov chains on a general state space in a random environment. We assume suitable versions of the standard drift and minorization conditions. In particular, the system dynamics should be contractive on the average with respect to the Lyapunov function and large enough small sets should exist with large enough minorization constants

Attraction to and repulsion from a subset of the unit sphere for isotropic stable Lévy processes Stoch. Process. their Appl. (IF 1.467) Pub Date : 20210420
Andreas E. Kyprianou, Sandra Palau, Tsogzolmaa SaizmaaTaking account of recent developments in the representation of ddimensional isotropic stable Lévy processes as selfsimilar Markov processes, we consider a number of new ways to condition its path. Suppose that S is a region of the unit sphere Sd−1={x∈Rd:x=1}. We construct the aforesaid stable Lévy process conditioned to approach S continuously from either inside or outside of the sphere. Additionally

Mean Euler characteristic of stationary random closed sets Stoch. Process. their Appl. (IF 1.467) Pub Date : 20210401
Jan RatajThe translative intersection formula of integral geometry yields an expression for the mean Euler characteristic of a stationary random closed set intersected with a fixed observation window. We formulate this result in the setting of sets with positive reach and using flag measures which yield curvature measures as marginals. As an application, we consider excursion sets of stationary random fields

Mixing time trichotomy in regenerating dynamic digraphs Stoch. Process. their Appl. (IF 1.467) Pub Date : 20210408
Pietro Caputo, Matteo QuattropaniWe study the convergence to stationarity for random walks on dynamic random digraphs with given degree sequences. The digraphs undergo full regeneration at independent geometrically distributed random time intervals with parameter α. Relaxation to stationarity is the result of an interplay of regeneration and mixing on the static digraph. When the number of vertices n tends to infinity and the parameter

Discretization of the Lamperti representation of a positive selfsimilar Markov process Stoch. Process. their Appl. (IF 1.467) Pub Date : 20210401
Jevgenijs Ivanovs, Jakob D. ThøstesenThis paper considers discretization of the Lévy process appearing in the Lamperti representation of a strictly positive selfsimilar Markov process. Limit theorems for the resulting approximation are established under some regularity assumptions on the given Lévy process. Additionally, the scaling limit of a positive selfsimilar Markov process at small times is provided. Finally, we present an application

The dynamics of stochastic monomolecular reaction systems in stochastic environments Stoch. Process. their Appl. (IF 1.467) Pub Date : 20210401
Daniele Cappelletti, Abhishek Pal Majumder, Carsten WiufWe study the stochastic dynamics of a system of interacting species in a stochastic environment by means of a continuoustime Markov chain with transition rates depending on the state of the environment. Models of gene regulation in systems biology take this form. We characterise the finitetime distribution of the Markov chain, provide conditions for ergodicity, and characterise the stationary distribution

Local theorems for (multidimensional) additive functionals of semiMarkov chains Stoch. Process. their Appl. (IF 1.467) Pub Date : 20210331
Artem Logachov, Anatolii Mogulskii, Evgeny Prokopenko, Anatoly YambartsevWe consider a (multidimensional) additive functional of semiMarkov chain, defined by an ergodic Markov chain with a finite number of states. The distribution of random vectors, governing the process, is supposed to be lattice and lighttailed. We derive the exact asymptotics in the local limit theorem. As a consequence, we establish a local central limit theorem.

LASSO estimation for spherical autoregressive processes Stoch. Process. their Appl. (IF 1.467) Pub Date : 20210401
Alessia Caponera, Claudio Durastanti, Anna VidottoThe purpose of the present paper is to investigate a class of spherical functional autoregressive processes in order to introduce and study LASSO (Least Absolute Shrinkage and Selection Operator) type estimators for the corresponding autoregressive kernels, defined in the harmonic domain by means of their spectral decompositions. Some crucial properties for these estimators are proved, in particular

Left–right crossings in the Miller–Abrahams random resistor network and in generalized Boolean models Stoch. Process. their Appl. (IF 1.467) Pub Date : 20210329
Alessandra Faggionato, Hlafo Alfie MimunWe consider random graphs G built on a homogeneous Poisson point process on Rd, d≥2, with points x marked by i.i.d. random variables Ex. Fixed a symmetric function h(⋅,⋅), the vertexes of G are given by points of the Poisson point process, while the edges are given by pairs {x,y} with x≠y and x−y≤h(Ex,Ey). We call G Poisson hgeneralized Boolean model, as one recovers the standard Poisson Boolean

Asymptotics for push on the complete graph Stoch. Process. their Appl. (IF 1.467) Pub Date : 20210329
Rami Daknama, Konstantinos Panagiotou, Simon ReisserWe study the classical randomized rumour spreading protocol push. Initially, a node in a graph possesses some information, which is then spread in a round based manner. In each round, each informed node chooses uniformly at random one of its neighbours and passes the information to it. The central quantity of interest is the runtime, that is, the number of rounds needed until every node has received

The extremal process of superBrownian motion Stoch. Process. their Appl. (IF 1.467) Pub Date : 20210326
YanXia Ren, Renming Song, Rui ZhangIn this paper, we establish limit theorems for the supremum of the support, denoted by Mt, of a supercritical superBrownian motion {Xt,t≥0} on R. We prove that there exists an m(t) such that (Xt−m(t),Mt−m(t)) converges in law, and give some large deviation results for Mt as t→∞. We also prove that the limit of the extremal process Et≔Xt−m(t) is a Poisson random measure with exponential intensity in

Characterizing limits and opportunities in speeding up Markov chain mixing Stoch. Process. their Appl. (IF 1.467) Pub Date : 20210322
Simon Apers, Alain Sarlette, Francesco TicozziA variety of paradigms have been proposed to speed up Markov chain mixing, ranging from nonbacktracking random walks to simulated annealing and lifted Metropolis–Hastings. We provide a general characterization of the limits and opportunities of different approaches for designing fast mixing dynamics on graphs using the framework of “lifted Markov chains”. This common framework allows to prove lower

Beta Laguerre processes in a high temperature regime Stoch. Process. their Appl. (IF 1.467) Pub Date : 20210322
Hoang Dung Trinh, Khanh Duy TrinhBeta Laguerre processes which are generalizations of the eigenvalue process of Wishart/Laguerre processes can be defined as the squares of radial Dunkl processes of type B. In this paper, we study the limiting behavior of their empirical measure processes. By the moment method, we show the convergence to a limit in a high temperature regime, a regime where βN→const∈(0,∞), where β is the inverse temperature