A Kawasaki dynamics in continuum is a dynamics of an infinite system of interacting particles in which randomly hop over the space. In this paper, we deal with an equilibrium Kawasaki dynamics which has a Gibbs measure [mu] as invariant measure. We study a diffusive limit of such a dynamics,...

We prove the existence of a weakly dependent strictly stationary solution of the equation Xt=F(Xt-1,Xt-2,Xt-3,...;[xi]t) called a chain with infinite memory. Here the innovations [xi]t constitute an independent and identically distributed sequence of random variables. The function F takes values...

This paper is concerned with the asymptotic behavior of sums of the form , where X is a 1-dimensional semimartingale and f a suitable test function, typically f(x)=xr, as [Delta]n--0. We prove a variety of "laws of large numbers", that is convergence in probability of Un(f)t, sometimes after...

We consider Sinai's walk in i.i.d. random scenery and focus our attention on a conjecture of Révész concerning the upper limits of Sinai's walk in random scenery when the scenery is bounded from above. A close study of the competition between the concentration property for Sinai's walk and...

Let X be a semi-fractional Brownian sheet, that is a centred and continuous Gaussian random field with . We provide, for [alpha][set membership, variant](0,2), an analysis of the propagation of singularities into the fractional direction of X. Here, singularities are times where the law of the...

In this paper we extend the notion of "filtration-consistent nonlinear expectation" (or "-consistent nonlinear expectation") to the case when it is allowed to be dominated by a g-expectation that may have a quadratic growth. We show that for such a nonlinear expectation many fundamental...

We develop some numerical schemes for d-dimensional stochastic differential equations derived from Milstein approximations of diffusions which are obtained by lifting the solutions of the stochastic differential equations to higher dimensional spaces using geometrical tools, in the line of the...

Cut an i.i.d. sequence (Xi) of 'letters' into 'words' according to an independent renewal process. Then one obtains an i.i.d. sequence of words, and thus the level 3 large deviation behaviour of this sequence of words is governed by the specific relative entropy. We consider the...

In this paper, we study reflected BSDE's with one continuous barrier, under monotonicity and general increasing conditions in y and non-Lipschitz conditions in z. We prove the existence and uniqueness of a solution by an approximation method.