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Mixing time trichotomy in regenerating dynamic digraphs Stoch. Process. their Appl. (IF 1.414) 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

Exponential mixing under controllability conditions for sdes driven by a degenerate Poisson noise Stoch. Process. their Appl. (IF 1.414) 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

Discretization of the Lamperti representation of a positive selfsimilar Markov process Stoch. Process. their Appl. (IF 1.414) 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 1.414) 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 1.414) 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 1.414) 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 1.414) 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 1.414) 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 1.414) 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 1.414) 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 1.414) 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

Asymptotic optimality of the generalized cμ rule under model uncertainty Stoch. Process. their Appl. (IF 1.414) Pub Date : 20210322
Asaf Cohen, Subhamay SahaWe consider a criticallyloaded multiclass queueing control problem with model uncertainty. The model consists of I types of customers and a single server. At any time instant, a decisionmaker (DM) allocates the server’s effort to the customers. The DM’s goal is to minimize a convex holding cost that accounts for the ambiguity with respect to the model, i.e., the arrival and service rates. For this

Mean Euler characteristic of stationary random closed sets Stoch. Process. their Appl. (IF 1.414) 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

Risk sensitive optimal stopping Stoch. Process. their Appl. (IF 1.414) Pub Date : 20210319
Damian Jelito, Marcin Pitera, Łukasz StettnerIn this paper we consider continuous time risk sensitive optimal stopping problem. Using the probabilistic approach and dyadic discrete time approximations we prove continuity of the generic optimal stopping value function for a large class of FellerMarkov processes. Also, we provide formulas for the corresponding optimal stopping policies and study regularity of approximating functions.

Maximal moments and uniform modulus of continuity for stable random fields Stoch. Process. their Appl. (IF 1.414) Pub Date : 20210304
Snigdha Panigrahi, Parthanil Roy, Yimin XiaoIn this work, we provide sharp bounds on the rate of growth of maximal moments for stationary symmetric stable random fields when the underlying nonsingular group action (or its restriction to a suitable lower rank subgroup) has a nontrivial dissipative component. We also investigate the relationship between this rate of growth and the path regularity properties of selfsimilar stable random fields

Dynamics of a Fleming–Viot type particle system on the cycle graph Stoch. Process. their Appl. (IF 1.414) Pub Date : 20210223
Josué CorujoWe study the Fleming–Viot particle process formed by N interacting continuoustime asymmetric random walks on the cycle graph, with uniform killing. We show that this model has a remarkable exact solvability, despite the fact that it is nonreversible with nonexplicit invariant distribution. Our main results include quantitative propagation of chaos and exponential ergodicity with explicit constants

Semilinear Kolmogorov equations on the space of continuous functions via BSDEs Stoch. Process. their Appl. (IF 1.414) Pub Date : 20210213
Federica Masiero, Carlo Orrieri, Gianmario Tessitore, Giovanni ZancoWe deal with a class of semilinear parabolic PDEs on the space of continuous functions that arise, for example, as Kolmogorov equations associated to the infinitedimensional lifting of pathdependent SDEs. We investigate existence of smooth solutions through their representation via forward–backward stochastic systems, for which we provide the necessary regularity theory. Because of the lack of smoothing

Concentration inequalities for additive functionals: A martingale approach Stoch. Process. their Appl. (IF 1.414) Pub Date : 20210204
Bob PepinThis work shows how exponential concentration inequalities for additive functionals of stochastic processes over a finite time interval can be derived from concentration inequalities for martingales. The approach is entirely probabilistic and naturally includes timeinhomogeneous and nonstationary processes as well as initial laws concentrated on a single point. The class of processes studied includes

Stochastic MHD equations with fractional kinematic dissipation and partial magnetic diffusion in R2 Stoch. Process. their Appl. (IF 1.414) Pub Date : 20210211
Jingna Li, Hongxia Liu, Hao TangThis paper focuses on a system of the 2D MHD equations with fractional kinematic dissipation and partial magnetic diffusion under random perturbations. We first establish the local existence, uniqueness and blowup criterion of pathwise classical solution to the corresponding SPDE with general multiplicative noise in R2. Moreover, when the noise is nonautonomous and linear, we further establish global

The domain of definition of the Lévy white noise Stoch. Process. their Appl. (IF 1.414) Pub Date : 20210215
Julien Fageot, Thomas HumeauIt is possible to construct Lévy white noises as generalized random processes in the sense of Gel’fand and Vilenkin, or as an independently scattered random measures introduced by Rajput and Rosinski. In this article, we unify those two approaches by extending the Lévy white noise Ẋ, defined as a generalized random process, to an independently scattered random measure. We are then able to give general

Nonequilibrium fluctuations of the weakly asymmetric normalized binary contact path process Stoch. Process. their Appl. (IF 1.414) Pub Date : 20210225
Xiaofeng Xue, Linjie ZhaoThis paper is a further investigation of the problem studied in Xue and Zhao (2020), where the authors proved a law of large numbers for the empirical measure of the weakly asymmetric normalized binary contact path process on Zd,d≥3, and then conjectured that a central limit theorem should hold under a nonequilibrium initial condition. We prove that the aforesaid conjecture is true when the dimension

Competing growth processes with random growth rates and random birth times Stoch. Process. their Appl. (IF 1.414) Pub Date : 20210224
Cécile Mailler, Peter Mörters, Anna SenkevichComparing individual contributions in a strongly interacting system of stochastic growth processes can be a very difficult problem. This is particularly the case when new growth processes are initiated depending on the state of previous ones and the growth rates of the individual processes are themselves random. We propose a novel technique to deal with such problems and show how it can be applied

Lyapunov criteria for uniform convergence of conditional distributions of absorbed Markov processes Stoch. Process. their Appl. (IF 1.414) Pub Date : 20210206
Nicolas Champagnat, Denis VillemonaisWe study the uniform convergence to quasistationarity of multidimensional processes absorbed when one of the coordinates vanishes. Our results cover competitive or weakly cooperative Lotka–Volterra birth and death processes and Feller diffusions with competitive Lotka–Volterra interaction. To this aim, we develop an original nonlinear Lyapunov criterion involving two functions, which applies to general

Dimensionfree Wasserstein contraction of nonlinear filters Stoch. Process. their Appl. (IF 1.414) Pub Date : 20210130
Nick WhiteleyFor a class of partially observed diffusions, conditions are given for the map from the initial condition of the signal to filtering distribution to be contractive with respect to Wasserstein distances, with rate which does not necessarily depend on the dimension of the statespace. The main assumptions are that the signal has affine drift and constant diffusion coefficient and that the likelihood

Sticky Bessel diffusions Stoch. Process. their Appl. (IF 1.414) Pub Date : 20210210
Goran PeskirWe consider a Bessel process X of dimension δ∈(0,2) having 0 as a slowly reflecting (sticky) boundary point with a stickiness parameter 1∕μ∈(0,∞). We show that (i) the process X can be characterised through its square Y=X2 as a unique weak solution to the SDE system dYt=δI(Yt>0)dt+2YtdBtI(Yt=0)dt=12μdℓt0(Y) where B is a standard Brownian motion and ℓ0(Y) is a diffusion local time process of Y at 0

A regularity theory for stochastic partial differential equations with a superlinear diffusion coefficient and a spatially homogeneous colored noise Stoch. Process. their Appl. (IF 1.414) Pub Date : 20210129
JaeHwan Choi, BeomSeok HanExistence, uniqueness, and regularity of a strong solution are obtained for stochastic PDEs with a colored noise F and its superlinear diffusion coefficient: du=(aijuxixj+biuxi+cu)dt+ξu1+λdF,(t,x)∈(0,∞)×Rd, where λ≥0 and the coefficients depend on (ω,t,x). The strategy of handling nonlinearity of the diffusion coefficient is to find a sharp estimation for a general Lipschitz case and apply it to

Partial derivative with respect to the measure and its application to general controlled meanfield systems Stoch. Process. their Appl. (IF 1.414) Pub Date : 20210122
Rainer Buckdahn, Yajie Chen, Juan LiLet (E,E) be an arbitrary measurable space. The paper first focuses on studying the partial derivative of a function f:P2,0(Rd×E)→R defined on the space of probability measures μ over (Rd×E,B(Rd)⊗E) whose first marginal μ1≔μ(⋅×E) has a finite second order moment. This partial derivative is taken with respect to q(dx,z), where μ has the disintegration μ(dxdz)=q(dx,z)μ2(dz) with respect to its second

Entrance laws for annihilating Brownian motions and the continuousspace voter model Stoch. Process. their Appl. (IF 1.414) Pub Date : 20210121
Matthias Hammer, Marcel Ortgiese, Florian VölleringConsider a system of particles moving independently as Brownian motions until two of them meet, when the colliding pair annihilates instantly. The construction of such a system of annihilating Brownian motions (aBMs) is straightforward as long as we start with a finite number of particles, but is more involved for infinitely many particles. In particular, if we let the set of starting points become

Nonsemimartingale solutions of reflected BSDEs and applications to Dynkin games Stoch. Process. their Appl. (IF 1.414) Pub Date : 20210118
Tomasz KlimsiakWe introduce a new class of reflected backward stochastic differential equations with two càdlàg barriers, which need not satisfy any separation conditions. For that reason, in general, the solutions are not semimartingales. We prove existence, uniqueness and approximation results for solutions of equations defined on general filtered probability spaces. Applications to nonlinear Dynkin games are given

Drift estimation on non compact support for diffusion models Stoch. Process. their Appl. (IF 1.414) Pub Date : 20210111
Fabienne Comte, Valentine GenonCatalotWe study non parametric drift estimation for an ergodic diffusion process from discrete observations. The drift is estimated on a set A using an approximate regression equation by a least squares contrast, minimized over finite dimensional subspaces of L2(A,dx). The novelty is that the set A is non compact and the diffusion coefficient unbounded. Risk bounds of a L2risk are provided where new variance

Metastability in a continuous meanfield model at low temperature and strong interaction Stoch. Process. their Appl. (IF 1.414) Pub Date : 20201231
K. Bashiri, G. MenzWe consider a system of N∈N meanfield interacting stochastic differential equations that are driven by Brownian noise and a singlesite potential of the form z↦z4∕4−z2∕2. The strength of the noise is measured by a small parameter ε>0 (which we interpret as the temperature), and we suppose that the strength of the interaction is given by J>0. Choosing the empirical mean (P:RN→R, Px=1∕N∑ixi) as the

Functional limit theorems for marked Hawkes point measures Stoch. Process. their Appl. (IF 1.414) Pub Date : 20201229
Ulrich Horst, Wei XuThis paper establishes a functional law of large numbers and a functional central limit theorem for marked Hawkes point measures and their corresponding shot noise processes. We prove that the normalized random measure can be approximated in distribution by the sum of a Gaussian white noise process plus an appropriate lifting map of a correlated onedimensional Brownian motion. The Brownian motion

Weak convergence and invariant measure of a full discretization for parabolic SPDEs with nonglobally Lipschitz coefficients Stoch. Process. their Appl. (IF 1.414) Pub Date : 20201224
Jianbo Cui, Jialin Hong, Liying SunWe propose a full discretization to approximate the invariant measure numerically for parabolic stochastic partial differential equations (SPDEs) with nonglobally Lipschitz coefficients. We present a priori estimates and regularity estimates of the numerical solution via a variational approach and Malliavin calculus. Under certain hypotheses, we present the timeindependent regularity estimates for

On regularity of functions of Markov chains Stoch. Process. their Appl. (IF 1.414) Pub Date : 20210101
Steven Berghout, Evgeny VerbitskiyWe consider processes which are functions of finitestate Markov chains. It is well known that such processes are rarely Markov. However, such processes are often regular in the following sense: the distant past values of the process have diminishing influence on the distribution of the present value. In the present paper, we present novel sufficient conditions for regularity of functions of Markov

Embedding of Walsh Brownian motion Stoch. Process. their Appl. (IF 1.414) Pub Date : 20201224
Erhan Bayraktar, Xin ZhangLet (Z,κ) be a Walsh Brownian motion with spinning measure κ. Suppose μ is a probability measure on Rn. We first provide a necessary and sufficient condition for μ to be a stopping distribution of (Z,κ). Then if the stopped process is required to be uniformly integrable, we show that such a stopping time exists if and only if μ is balanced. Next, under the assumption of being balanced, we identify

Asymptotic approach for backward stochastic differential equation with singular terminal condition Stoch. Process. their Appl. (IF 1.414) Pub Date : 20201218
Paulwin Graewe, Alexandre PopierIn this paper, we provide a onetoone correspondence between the solution Y of a BSDE with singular terminal condition and the solution H of a BSDE with singular generator. This result provides the precise asymptotic behaviour of Y close to the final time and enlarges the uniqueness result to a wider class of generators.

The shape of the value function under Poisson optimal stopping Stoch. Process. their Appl. (IF 1.414) Pub Date : 20201205
David HobsonIn a classical problem for the stopping of a diffusion process (Xt)t≥0, where the goal is to maximise the expected discounted value of a function of the stopped process Ex[e−βτg(Xτ)], maximisation takes place over all stopping times τ. In a Poisson optimal stopping problem, stopping is restricted to event times of an independent Poisson process. In this article we consider whether the resulting value

Locally Feller processes and martingale local problems Stoch. Process. their Appl. (IF 1.414) Pub Date : 20201130
Mihai Gradinaru, Tristan HaugomatThis paper is devoted to the study of a certain type of martingale problems associated to general operators corresponding to processes which have finite lifetime. We analyse several properties and in particular the weak convergence of sequences of solutions for an appropriate Skorokhod topology setting. We point out the Fellertype features of the associated solutions to this type of martingale problem

Extremes of locally stationary Gaussian and chi fields on manifolds Stoch. Process. their Appl. (IF 1.414) Pub Date : 20201203
Wanli QiaoDepending on a parameter h∈(0,1], let {Xh(t),t∈Mh} be a class of centered Gaussian fields indexed by compact manifolds Mh with positive reach. For locally stationary Gaussian fields Xh, we study the asymptotic excursion probabilities of Xh on Mh. Two cases are considered: (i) h is fixed and (ii) h→0. These results are also extended to obtain the limit behaviors of the extremes of locally stationary

Martingale driven BSDEs, PDEs and other related deterministic problems Stoch. Process. their Appl. (IF 1.414) Pub Date : 20201205
Adrien Barrasso, Francesco RussoWe focus on a class of BSDEs driven by a càdlàg martingale and the corresponding Markovian BSDEs which arise when the randomness of the driver appears through a Markov process. To those BSDEs we associate a deterministic equation which, when the Markov process is a Brownian diffusion, is nothing else but a parabolic semilinear PDE. We prove existence and uniqueness of a decoupled mild solution of

On the center of mass of the elephant random walk Stoch. Process. their Appl. (IF 1.414) Pub Date : 20201203
Bernard Bercu, Lucile LaulinOur goal is to investigate the asymptotic behavior of the center of mass of the elephant random walk, which is a discretetime random walk on integers with a complete memory of its whole history. In the diffusive and critical regimes, we establish the almost sure convergence, the law of iterated logarithm and the quadratic strong law for the center of mass of the elephant random walk. The asymptotic

Inhomogeneous functionals and approximations of invariant distributions of ergodic diffusions: Central limit theorem and moderate deviation asymptotics Stoch. Process. their Appl. (IF 1.414) Pub Date : 20201117
Arnab Ganguly, P. SundarThe paper studies asymptotics of inhomogeneous integral functionals of an ergodic diffusion process under the effect of discretization. Convergence to the corresponding functionals of the invariant distribution is shown for suitably chosen discretization steps, and the fluctuations are analyzed through central limit theorem and moderate deviation principle. The results will be particularly useful for

Hypothesis testing for a Lévydriven storage system by Poisson sampling Stoch. Process. their Appl. (IF 1.414) Pub Date : 20201130
M. Mandjes, L. RavnerThis paper focuses on hypothesis testing for the input of a Lévydriven storage system by sampling of the storage level. As the likelihood is not explicit we propose two tests that rely on transformation of the data. The first approach uses i.i.d. ‘quasibusyperiods’ between observations of zero workload. The distribution of the duration of quasibusyperiods is determined. The second method is a

Quasilinear Stochastic PDEs with two obstacles: Probabilistic approach Stoch. Process. their Appl. (IF 1.414) Pub Date : 20201126
Laurent Denis, Anis Matoussi, Jing ZhangWe prove an existence and uniqueness result for twoobstacle problem for quasilinear Stochastic PDEs (DOSPDEs for short). The method is based on the probabilistic interpretation of the solution by using the backward doubly stochastic differential equations (BDSDEs for short).

General multilevel adaptations for stochastic approximation algorithms II: CLTs Stoch. Process. their Appl. (IF 1.414) Pub Date : 20201125
Steffen DereichIn this article we establish central limit theorems for multilevel Polyak–Ruppert averaged stochastic approximation schemes. We work under very mild technical assumptions and consider the slow regime in which typical errors decay like N−δ with δ∈(0,12) and the critical regime in which errors decay of order N−1∕2logN in the runtime N of the algorithm.

Approximation of the allelic frequency spectrum in general supercritical branching populations Stoch. Process. their Appl. (IF 1.414) Pub Date : 20201113
Benoit HenryWe consider a branching population with arbitrary lifetime distribution and Poissonian births. Moreover, individuals experience mutations at Poissonian rate. This mechanism leads to a partition of the population by type: the allelic partition. We focus on the frequency spectrum A(k,t) which counts the number of families of size k at time t. Our main goal is to study the asymptotic error made in some

Asymptotic analysis of model selection criteria for general hidden Markov models Stoch. Process. their Appl. (IF 1.414) Pub Date : 20201106
Shouto Yonekura, Alexandros Beskos, Sumeetpal S. SinghThe paper obtains analytical results for the asymptotic properties of Model Selection Criteria – widely used in practice – for a general family of hidden Markov models (HMMs), thereby substantially extending the related theory beyond typical ‘i.i.d.like’ model structures and filling in an important gap in the relevant literature. In particular, we look at the Bayesian and Akaike Information Criteria

On the identifiability of interaction functions in systems of interacting particles Stoch. Process. their Appl. (IF 1.414) Pub Date : 20201103
Zhongyang Li, Fei Lu, Mauro Maggioni, Sui Tang, Cheng ZhangWe address a fundamental issue in the nonparametric inference for systems of interacting particles: the identifiability of the interaction functions. We prove that the interaction functions are identifiable for a class of firstorder stochastic systems, including linear systems with general initial laws and nonlinear systems with stationary distributions. We show that a coercivity condition is sufficient

Quasistationary distributions for subcritical superprocesses Stoch. Process. their Appl. (IF 1.414) Pub Date : 20201101
Rongli Liu, YanXia Ren, Renming Song, Zhenyao SunSuppose that X is a subcritical superprocess. Under some asymptotic conditions on the mean semigroup of X, we prove the Yaglom limit of X exists and identify all quasistationary distributions of X.

A lower bound on the displacement of particles in 2D Gibbsian particle systems Stoch. Process. their Appl. (IF 1.414) Pub Date : 20201013
Michael Fiedler, Thomas RichthammerWhile 2D Gibbsian particle systems might exhibit orientational order resulting in a latticelike structure, these particle systems do not exhibit positional order if the interaction between particles satisfies some weak assumptions. Here we investigate to which extent particles within a box of size 2n×2n may fluctuate from their ideal lattice position. We show that particles near the center of the

Statistical inference of subcritical strongly stationary Galton–Watson processes with regularly varying immigration Stoch. Process. their Appl. (IF 1.414) Pub Date : 20201016
Mátyás Barczy, Bojan Basrak, Péter Kevei, Gyula Pap, Hrvoje PlaninićWe describe the asymptotic behavior of the conditional least squares estimator of the offspring mean for subcritical strongly stationary Galton–Watson processes with regularly varying immigration with tail index α∈(1,2). The limit law is the ratio of two dependent stable random variables with indices α∕2 and 2α∕3, respectively, and it has a continuously differentiable density function. We use point

Wellposedness and approximation of some onedimensional Lévydriven nonlinear SDEs Stoch. Process. their Appl. (IF 1.414) Pub Date : 20201023
Noufel Frikha, Libo LiIn this article, we are interested in the strong wellposedness together with the numerical approximation of some onedimensional stochastic differential equations with a nonlinear drift, in the sense of McKean–Vlasov, driven by a spectrallypositive Lévy process and a Brownian motion. We provide criteria for the existence of strong solutions under nonLipschitz conditions of Yamada–Watanabe type

Local times and sample path properties of the Rosenblatt process Stoch. Process. their Appl. (IF 1.414) Pub Date : 20201013
George Kerchev, Ivan Nourdin, Eero Saksman, Lauri ViitasaariLet Z=(Zt)t≥0 be the Rosenblatt process with Hurst index H∈(1∕2,1). We prove joint continuity for the local time of Z, and establish Hölder conditions for the local time. These results are then used to study the irregularity of the sample paths of Z. Based on analogy with similar known results in the case of fractional Brownian motion, we believe our results are sharp. A main ingredient of our proof

Itô’s formula for jump processes in Lpspaces Stoch. Process. their Appl. (IF 1.414) Pub Date : 20201009
István Gyöngy, Sizhou WuWe present an Itô formula for the Lpnorm of jump processes having stochastic differentials in Lpspaces. The main results extend wellknown theorems of Krylov to the case of processes with jumps, which can be used to prove existence and uniqueness theorems in Lpspaces for SPDEs driven by Lévy processes.

Bivariate Bernstein–gamma functions and moments of exponential functionals of subordinators Stoch. Process. their Appl. (IF 1.414) Pub Date : 20201010
A. Barker, M. SavovIn this paper, we extend recent work on the class of Bernstein–gamma functions to the class of bivariate Bernstein–gamma functions. In the more general bivariate setting, we determine Stirlingtype asymptotic bounds which generalise, improve upon, and streamline those found for univariate Bernstein–gamma functions. Then, we demonstrate the importance and power of these results through an application

On the strong Markov property for stochastic differential equations driven by GBrownian motion Stoch. Process. their Appl. (IF 1.414) Pub Date : 20201007
Mingshang Hu, Xiaojun Ji, Guomin LiuThe objective of this paper is to study the strong Markov property for the stochastic differential equations driven by GBrownian motion (GSDEs for short). We first extend the deterministictime conditional Gexpectation to optional times. The strong Markov property for GSDEs is then obtained by Kolmogorov’s criterion for tightness. In particular, for any given optional time τ and GBrownian motion

The value of insider information for superreplication with quadratic transaction costs Stoch. Process. their Appl. (IF 1.414) Pub Date : 20201010
Yan Dolinsky, Jonathan ZouariWe study superreplication of European contingent claims in an illiquid market with insider information. Illiquidity is captured by quadratic transaction costs and insider information is modeled by an investor who can peek into the future. Our main result describes the scaling limit of the superreplication prices when the number of trading periods increases to infinity. Moreover, the scaling limit

Optimal lower bounds on hitting probabilities for nonlinear systems of stochastic fractional heat equations Stoch. Process. their Appl. (IF 1.414) Pub Date : 20200919
Robert C. Dalang, Fei PuWe consider a system of d nonlinear stochastic fractional heat equations in spatial dimension 1 driven by multiplicative ddimensional space–time white noise. We establish a sharp Gaussiantype upper bound on the twopoint probability density function of (u(s,y),u(t,x)). From this result, we deduce optimal lower bounds on hitting probabilities of the process {u(t,x):(t,x)∈[0,∞[×R} in the nonGaussian

Hamilton cycles and perfect matchings in the KPKVB model Stoch. Process. their Appl. (IF 1.414) Pub Date : 20200917
Nikolaos Fountoulakis, Dieter Mitsche, Tobias Müller, Markus SchepersIn this paper we consider the existence of Hamilton cycles and perfect matchings in a random graph model proposed by Krioukov et al. in 2010. In this model, nodes are chosen randomly inside a disk in the hyperbolic plane and two nodes are connected if they are at most a certain hyperbolic distance from each other. It has been previously shown that this model has various properties associated with complex

Quaternionic stochastic areas Stoch. Process. their Appl. (IF 1.414) Pub Date : 20200929
Fabrice Baudoin, Nizar Demni, Jing WangWe define and study quaternionic stochastic areas processes associated with Brownian motions on the quaternionic rankone symmetric spaces HHn and HPn. The characteristic functions of fixedtime marginals of these processes are computed and allow for the explicit description of their corresponding largetime limits. We also obtain exact formulas for the semigroup densities of the stochastic area processes