Weak convergence to a form of fractional Brownian motion is established for a wide class of nonstationary fractionally integrated multivariate processes. Instrumental for the main argument is a result of some independent interest on approximations for partial sums of stationary linear vector...

In this paper we introduce a stochastic integral with respect to the process where 0[alpha]1/2, and Wt is a Brownian motion. Sufficient integrability conditions are deduced using the techniques of the Malliavin calculus and the notion of fractional derivative. We study continuity properties of...

We provide moment inequalities and sufficient conditions for the quick convergence for Markov random walks, without the assumption of uniform ergodicity for the underlying Markov chain. Our approach is based on martingales associated with the Poisson equation and Wald equations for the second...

Let [alpha] and [beta] be positive constants. Let X be the supercritical super-Brownian motion corresponding to the evolution equation in and let Z be the binary branching Brownian-motion with branching rate [beta]. For t[greater-or-equal, slanted]0, let , that is R(t) is the (accumulated)...

Using the limit theorem for stochastic integral obtained by Jakubowski et al. (Probab. Theory Related Fields 81 (1989) 111-137), we introduce in this paper a new method for proving weak convergence results of empirical processes by a martingale method which allows discontinuities for the...

Under smooth assumptions and notably the Isaacs's condition on the Hamiltonian, we prove the existence of a saddle-point for the "mixed" zero-sum stochastic differential game with payoffThe main tool is the notion of double barrier reflected backward SDEs.

We introduce several martingale changes of measure of the law of the exit measure of super Brownian motion. We represent these laws in terms of "immortal particle" branching processes with immigration of mass, and relate them to the study of solutions to Lu=cu2 in D. The changes of measure...

We have considered the problem of the weak convergence, as [var epsilon] tends to zero, of the multiple integral processesin the space , where f[set membership, variant]L2([0,T]n) is a given function, and {[eta][var epsilon](t)}[var epsilon]0 is a family of stochastic processes with absolutely...

Let {Xj}j=1[infinity] be a stationary Gaussian sequence of random vectors with mean zero. We study the convergence in distribution of an-1[summation operator]j=1n (G(Xj)-E[G(Xj)]), where G is a real function in with finite second moment and {an} is a sequence of real numbers converging to...

The aim of this work is the study of limit points of Gaussian processes with continuous paths defined by an integral representation. Precisely, we control the asymptotic behaviour of a(t)Xt, where a is a function which vanishes at infinity and X is a Gaussian process. At first, we study...