The paper deals with the Cauchy problem in of a stochastic heat equation . The locally lipschitz drift coefficient f can have polynomial growth while the diffusion coefficient [sigma] is supposed to be lipschitz but not necessarily bounded. Of course, for the existence of a solution alone, a...

The random average process is a randomly evolving d-dimensional surface whose heights are updated by random convex combinations of neighboring heights. The fluctuations of this process in case of linear initial conditions have been studied before. In this paper, we analyze the case of polynomial...

In the paper Bally and Pagès (2000) an algorithm based on an optimal discrete quantization tree is designed to compute the solution of multi-dimensional obstacle problems for homogeneous -valued Markov chains (Xk)0[less-than-or-equals, slant]k[less-than-or-equals, slant]n. This tree is made up...

The Euler scheme is a well-known method of approximation of solutions of stochastic differential equations (SDEs). A lot of results are now available concerning the precision of this approximation in case of equations driven by a drift and a Brownian motion. More recently, people got interested...

Let T=(T1,T2,T3,...) be a sequence of real random variables. We investigate the following fixed point equation for distributions [mu]: W[congruent with][summation operator]j=1[infinity] TjWj, where W,W1,W2,... have distribution [mu] and T,W1,W2,... are independent. The corresponding functional...

This paper gives the asymptotic theory of a class of rank order statistics {TN} for two-sample problem pertaining to empirical processes based on the squared residuals from two classes of ARCH models. An important aspect is that, unlike the residuals of ARMA models, the asymptotics of {TN}...

We propose a new approach to study the stability of the optimal filter w.r.t. its initial condition, by introducing a "robust" filter, which is exponentially stable and which approximates the optimal filter uniformly in time. The "robust" filter is obtained here by truncation of the likelihood...

We compare three dependence coefficients expressed in terms of conditional expectations, and we study their behaviour in various situations. Next, we give a new covariance inequality involving the weakest of those coefficients, and we compare this bound to that obtained by Rio (Ann. Inst. H....

Matzinger (Random Structure Algorithm 15 (1999a) 196) showed how to reconstruct almost every three color scenery, that is a coloring of the integers with three colors, by observing it along the path of a simple random walk, if this scenery is the outcome of an i.i.d. process. This reconstruction...

We prove a stochastic representation, similar to the Feynman-Kac formula, for solutions of parabolic equations involving a distribution expressed as divergence of a measurable field. This leads to an extension of the method of backward stochastic differential equations to a class of...