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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

Drift estimation on non compact support for diffusion models Stoch. Process. their Appl. (IF 1.414) Pub Date : 20210111
F. Comte; V. 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

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

The effect of graph connectivity on metastability in a stochastic system of spiking neurons Stoch. Process. their Appl. (IF 1.414) Pub Date : 20200922
Morgan André; Léo PlancheWe consider a continuoustime stochastic model of spiking neurons originally introduced by Ferrari et al. in Ferrari et al. (2018). In this model, we have a finite or countable number of neurons which are vertices in some graph G where the edges indicate the synaptic connection between them. We focus on metastability, understood as the property for the time of extinction of the network to be asymptotically

Simulated annealing in Rd with slowly growing potentials Stoch. Process. their Appl. (IF 1.414) Pub Date : 20200925
Pierre Monmarché; Nicolas Fournier; Camille TardifWe use a localization procedure to weaken the growth assumptions of Royer (1989), Miclo (1992) and Zitt (2008) concerning the continuoustime simulated annealing in Rd. We show that a transition occurs for potentials growing like aloglogx at infinity. We also study a class of potentials with possibly unbounded sets of local minima.

Particles Systems for mean reflected BSDEs Stoch. Process. their Appl. (IF 1.414) Pub Date : 20200912
Philippe Briand; Hélène HibonIn this paper, we study Reflected Backward Stochastic Differential Equations for which the constraint is not on the paths of the solution but on its law as introduced by Briand, Elie and Hu in Briand et al. (2018). We extend the recent work Briand et al. (2020) of Briand, Chaudru de Raynal, Guillin and Labart on the chaos propagation for mean reflected SDEs to the backward framework. When the driver

Estimation of α, β and portfolio weights in a purejump model with long memory in volatility Stoch. Process. their Appl. (IF 1.414) Pub Date : 20200925
Yichen Zhang; Clifford M. HurvichWe investigate a bivariate purejump model of stock prices with long memory in volatility, using a marked logGaussian Cox process. We show that, due to the nonsynchronicity of transactions, the ordinary least squares estimator of the slope in a contemporaneous regression of returns on returns converges to different targets depending on the sampling frequency. Therefore, we propose a transactionlevel

On sets of zero stationary harmonic measure Stoch. Process. their Appl. (IF 1.414) Pub Date : 20200919
Eviatar B. Procaccia; Yuan ZhangIn this paper, we study properties of the stationary harmonic measure which are unique to the stationary case. We prove that any subset with an appropriate sublinear horizontal growth has a nonzero stationary harmonic measure. On the other hand, we show that any subset with at least linear horizontal growth will have a 0 stationary harmonic measure at every point. This result is fundamental to any

Asymptotic optimality of degreegreedy discovering of independent sets in Configuration Model graphs Stoch. Process. their Appl. (IF 1.414) Pub Date : 20200912
Matthieu Jonckheere; Manuel SáenzFinding independent sets of maximum size in fixed graphs is well known to be an NPhard task. Using scaling limits, we characterise the asymptotics of sequential degreegreedy explorations and provide sufficient conditions for this algorithm to find an independent set of asymptotically optimal size in large sparse random graphs with given degree sequences. In the special case of sparse Erdös–Rényi

Truncated moments of perpetuities and a new central limit theorem for GARCH processes without Kesten’s regularity Stoch. Process. their Appl. (IF 1.414) Pub Date : 20200912
Adam Jakubowski; Zbigniew S. SzewczakWe consider a class of perpetuities which admit direct characterization of asymptotics of the key truncated moment. The class contains perpetuities without polynomial decay of tail probabilities thus not satisfying Kesten’s theorem. We show how to apply this result in deriving a new weak law of large numbers for solutions to stochastic recurrence equations and a new central limit theorem for GARCH(1

The almost sure semicircle law for random band matrices with dependent entries Stoch. Process. their Appl. (IF 1.414) Pub Date : 20200912
Michael Fleermann; Werner Kirsch; Thomas KriecherbauerWe analyze the empirical spectral distribution of random periodic band matrices with correlated entries. The correlation structure we study was first introduced in Hochstättler et al. (2015) by Hochstättler, Kirsch and Warzel, who named their setup almost uncorrelated and showed convergence to the semicircle distribution in probability. We strengthen their results which turn out to be also valid almost

Discretetime TASEP with holdback Stoch. Process. their Appl. (IF 1.414) Pub Date : 20200912
Seva Shneer; Alexander StolyarWe study the following interacting particle system. There are ρn particles, ρ<1, moving clockwise (“right”), in discrete time, on n sites arranged in a circle. Each site may contain at most one particle. At each time, a particle may move to the rightneighbor site according to the following rules. If its rightneighbor site is occupied by another particle, the particle does not move. If the particle

MFGs for partially reversible investment Stoch. Process. their Appl. (IF 1.414) Pub Date : 20200919
Haoyang Cao; Xin GuoThis paper analyzes a class of infinitetimehorizon stochastic games with singular controls motivated from the partially reversible problem. It provides an explicit solution for the meanfield game (MFG), and presents sensitivity analysis to compare the solution for the MFG with that for the singleagent control problem. It shows that in the MFG, model parameters not only affect the optimal strategies

The rencontre problem Stoch. Process. their Appl. (IF 1.414) Pub Date : 20200919
F. Thomas Bruss; Philip A. Ernst; Dongzhou HuangLet Xk1k=1∞,Xk2k=1∞,…,Xkdk=1∞ be d independent sequences of Bernoulli random variables with successparameters p1,p2,…,pd respectively, where d≥2 is a positive integer, and 0

Martingale representation in the enlargement of the filtration generated by a point process Stoch. Process. their Appl. (IF 1.414) Pub Date : 20200912
Paolo Di Tella, Monique JeanblancLet X be a point process and let X denote the filtration generated by X. In this paper we study martingale representation theorems in the filtration G obtained as an initial and progressive enlargement of the filtration X. The progressive enlargement is done here by means of a whole point process H. We do not require further assumptions on the point process H nor on the dependence between X and H.

Wellposedness of scalar BSDEs with subquadratic generators and related PDEs Stoch. Process. their Appl. (IF 1.414) Pub Date : 20200910
Shengjun Fan, Ying HuWe first establish the existence of an unbounded solution to a backward stochastic differential equation (BSDE) with generator g allowing a general growth in the state variable y and a subquadratic growth in the state variable z, when the terminal condition satisfies a subexponential moment integrability condition, which is weaker than the usual exp(μL)integrability and stronger than Lp(p>1)integrability

Heat kernel analysis on diamond fractals Stoch. Process. their Appl. (IF 1.414) Pub Date : 20200909
Patricia Alonso RuizThis paper presents a detailed analysis of the heat kernel on an (N×N)parameter family of compact metric measure spaces which do not satisfy the volume doubling property. In particular, uniform bounds of the heat kernel, its Lipschitz continuity and the continuity of the corresponding heat semigroup are studied; a specific example is presented revealing a logarithmic correction. The estimates are

On the optimality of double barrier strategies for Lévy processes Stoch. Process. their Appl. (IF 1.414) Pub Date : 20200909
Kei NobaThis paper studies de Finetti’s optimal dividend problem with capital injection. We confirm the optimality of a double barrier strategy when the underlying risk model follows a Lévy process that may have positive and negative jumps. In contrast with the spectrally onesided cases, double barrier strategies cannot be handled by using scale functions to obtain some properties of the expected net present

The Breuer–Major theorem in total variation: Improved rates under minimal regularity Stoch. Process. their Appl. (IF 1.414) Pub Date : 20200905
Ivan Nourdin, David Nualart, Giovanni PeccatiIn this paper we prove an estimate for the total variation distance, in the framework of the Breuer–Major theorem, using the Malliavin–Stein method, assuming the underlying function g to be once weakly differentiable with g and g′ having finite moments of order four with respect to the standard Gaussian density. This result is proved by a combination of Gebelein’s inequality and some novel estimates

Random walk in changing environment Stoch. Process. their Appl. (IF 1.414) Pub Date : 20200828
Gideon Amir; Itai Benjamini; Ori GurelGurevich; Gady KozmaWe introduce the notion of Random Walk in Changing Environment (RWCE) a random walk on a weighted graph in which the weights may change between steps. RWCE’s generalize many known RW (e.g. reinforced RW, true SAW). We explore possible properties of RWCE’s, and provide criteria for recurrence and transience when the underlying graph is N or a tree. We construct a RWCE on Z2 where conductances can only

Lévydriven causal CARMA random fields Stoch. Process. their Appl. (IF 1.414) Pub Date : 20200824
Viet Son PhamWe introduce Lévydriven causal CARMA random fields on Rd, extending the class of CARMA processes. The definition is based on a system of stochastic partial differential equations which generalize the classical statespace representation of CARMA processes. The resulting CARMA model differs fundamentally from the CARMA random field of Brockwell and Matsuda. We show existence of the model under mild

Transition time asymptotics of queuebased activation protocols in randomaccess networks Stoch. Process. their Appl. (IF 1.414) Pub Date : 20200824
S.C. Borst; F. den Hollander; F.R. Nardi; M. SfragaraWe consider networks where each node represents a server with a queue. An active node deactivates at unit rate. An inactive node activates at a rate that depends on its queue length, provided none of its neighbors is active. For complete bipartite networks, in the limit as the queues become large, we compute the average transition time between the two states where one half of the network is active

Scaling transition and edge effects for negatively dependent linear random fields on Z2 Stoch. Process. their Appl. (IF 1.414) Pub Date : 20200819
Donatas SurgailisWe obtain a complete description of anisotropic scaling limits and the existence of scaling transition for a class of negatively dependent linear random fields X on Z2 with movingaverage coefficients a(t,s) decaying as t−q1 and s−q2 in the horizontal and vertical directions, q1−1+q2−1<1 and satisfying ∑(t,s)∈Z2a(t,s)=0. The scaling limits are taken over rectangles whose sides increase as λ and

Random dynamics of pLaplacian lattice systems driven by infinitedimensional nonlinear noise Stoch. Process. their Appl. (IF 1.414) Pub Date : 20200814
Renhai Wang; Bixiang WangThis article is concerned with the global existence and random dynamics of the nonautonomous pLaplacian lattice system defined on the entire integer set driven by infinitedimensional nonlinear noise. The existence and uniqueness of mean square solutions to the equations are proved when the nonlinear drift and diffusion terms are locally Lipschitz continuous. It is shown that the mean random dynamical

SPDEs with linear multiplicative fractional noise: Continuity in law with respect to the Hurst index Stoch. Process. their Appl. (IF 1.414) Pub Date : 20200814
Luca M. Giordano; Maria Jolis; Lluís QuerSardanyonsIn this article, we consider the onedimensional stochastic wave and heat equations driven by a linear multiplicative Gaussian noise which is white in time and behaves in space like a fractional Brownian motion with Hurst index H∈(14,1). We prove that the solution of each of the above equations is continuous in terms of the index H, with respect to the convergence in law in the space of continuous

Exit times for semimartingales under nonlinear expectation Stoch. Process. their Appl. (IF 1.414) Pub Date : 20200807
Guomin LiuLet Eˆ be the upper expectation of a weakly compact but possibly nondominated family P of probability measures. Assume that Y is a ddimensional Psemimartingale under Eˆ. Given an open set Q⊂Rd, the exit time of Y from Q is defined by τQ≔inf{t≥0:Yt∈Qc}.The main objective of this paper is to study the quasicontinuity properties of τQ under the nonlinear expectation Eˆ. Under some additional assumptions

Invasion and fixation of microbial dormancy traits under competitive pressure Stoch. Process. their Appl. (IF 1.414) Pub Date : 20200807
Jochen Blath; András TóbiásMicrobial dormancy is an evolutionary trait that has emerged independently at various positions across the tree of life. It describes the ability of a microorganism to switch to a metabolically inactive state that can withstand unfavorable conditions. However, maintaining such a trait requires additional resources that could otherwise be used to increase e.g. reproductive rates. In this paper, we aim

A solution technique for Lévy driven long term average impulse control problems Stoch. Process. their Appl. (IF 1.414) Pub Date : 20200806
Sören Christensen; Tobias SohrThis article treats long term average impulse control problems with running costs in the case that the underlying process is a Lévy process. Assuming a maximum representation for the payoff function, we give easy to verify conditions for the control problem to have an s,S strategy as an optimizer. The occurring thresholds are given by the roots of an explicit auxiliary function. This leads to a step

The stochastic thinfilm equation: Existence of nonnegative martingale solutions Stoch. Process. their Appl. (IF 1.414) Pub Date : 20200729
Benjamin Gess; Manuel V. GnannWe consider the stochastic thinfilm equation with colored Gaussian Stratonovich noise in one space dimension and establish the existence of nonnegative weak (martingale) solutions. The construction is based on a TrotterKatotype decomposition into a deterministic and a stochastic evolution, which yields an easy to implement numerical algorithm. Compared to previous work, no interface potential has

Forward and backward stochastic differential equations with normal constraints in law Stoch. Process. their Appl. (IF 1.414) Pub Date : 20200729
Philippe Briand; Pierre Cardaliaguet; PaulÉric Chaudru de Raynal; Ying HuIn this paper we investigate the wellposedness of backward or forward stochastic differential equations whose law is constrained to live in an a priori given (smooth enough) set and which is reflected along the corresponding “normal” vector. We also study the associated interacting particle system reflected in mean field and asymptotically described by such equations. The case of particles submitted

Semigroup properties of solutions of SDEs driven by Lévy processes with independent coordinates Stoch. Process. their Appl. (IF 1.414) Pub Date : 20200724
Tadeusz Kulczycki; Michał RyznarWe study the stochastic differential equation dXt=A(Xt−)dZt, X0=x, where Zt=(Zt(1),…,Zt(d))T and Zt(1),…,Zt(d) are independent onedimensional Lévy processes with characteristic exponents ψ1,…,ψd. We assume that each ψi satisfies a weak lower scaling condition WLSC(α,0,C̲), a weak upper scaling condition WUSC(β,1,C¯) (where 0<α≤β<2) and some additional regularity properties. We consider two mutually

Tier structure of strongly endotactic reaction networks Stoch. Process. their Appl. (IF 1.414) Pub Date : 20200724
David F. Anderson; Daniele Cappelletti; Jinsu Kim; Tung D. NguyenReaction networks are mainly used to model the timeevolution of molecules of interacting chemical species. Stochastic models are typically used when the counts of the molecules are low, whereas deterministic models are often used when the counts are in high abundance. The mathematical study of reaction networks has increased dramatically over the last two decades as these models are now routinely