We consider zero-range processes with jump rate g(x)=x[gamma] for 0[gamma]=1. We obtain that for the local process confined to a cube in of width n, the spectral gap is bounded below by positive multiple of (n2(1+[rho])1-[gamma])-1, where [rho]=k/(2n+1)d and k is the total number of particles in...

We establish Donnelly-Kurtz-type particle representations for a class of superprocesses with dependent spatial motions, and for a sequence of such superprocesses we prove convergence of the finite-dimensional distributions given convergence of the motion processes. As special cases, we construct...

In this article, we give sharp bounds for the Euler discretization of the Lévy area associated to a d-dimensional fractional Brownian motion. We show that there are three different regimes for the exact root mean square convergence rate of the Euler scheme, depending on the Hurst parameter...

We analyze the number of zeros of det(F([alpha])), where F([alpha]) is the matrix exponent of a Markov Additive Process (MAP) with one-sided jumps. The focus is on the number of zeros in the right half of the complex plane, where F([alpha]) is analytic. In addition, we also consider the case of...

In quantum physics, recent investigations deal with the so-called "stochastic Schrodinger equations" theory. This concerns stochastic differential equations of non-usual-type describing random evolutions of open quantum systems. These equations are often justified with heuristic rules and pose...

We are interested in the genealogical structure of alleles for a Bienaymé-Galton-Watson branching process with neutral mutations (infinite alleles model), in the situation where the initial population is large and the mutation rate small. We shall establish that for an appropriate regime, the...

In this paper, we prove the Poincaré inequality and the integration by parts formula for the invariant measure of the linear SPDE driven by Lévy Noise. The equation was researched in Dong and Xie [5], which has proved the existence and uniqueness of the weak solution and the ergodicity of...

We consider local martingales of exponential form or , where X denotes one component of a multivariate affine process. We give a weak sufficient criterion for M to be a true martingale. As a first application, we derive a simple sufficient condition for absolute continuity of the laws of two...

We propose a generic framework for the analysis of Monte Carlo simulation schemes of backward SDEs. The general results are used to re-visit the convergence of the algorithm suggested by Bouchard and Touzi (2004) [6]. By keeping the higher order terms in the expansion of the Skorohod integrals...

We consider stochastic equations of the prototype on a smooth domain , with Dirichlet boundary condition, where [beta], [kappa] are positive constants and {Wt,t=0} is a one-dimensional standard Wiener process. We estimate the probability of finite-time blowup of positive solutions, as well as...