Let us consider the following stochastic differential equation:where (Bt)t[greater-or-equal, slanted]0 is a d-dimensional brownian motion starting at 0 and b a function from to which is a gradient field. We aim at studying the convergence rate of the semi-group associated to (E) to its invariant...

We study the weak limit behavior of certain types of point processes obtained by replacing the original observations by the bootstrap sample. The usual bootstrap fails asymptotically in cases for which there exists a Poisson point process or a fixed point measure in the limit. In some cases, by...

We prove the existence of a two-parameter symmetric Markov process associated with the Bessel process in of dimension d[greater-or-equal, slanted]2. This process is constructed as a one-parameter process in the space which is viewed as the path space of the Bessel process. The method consists in...

The martingale problems provide a powerful tool for characterizing Markov processes, especially in addressing convergence issues. For each n, let metric space E-valued process Xn be a solution of the martingale problems (i.e.is a martingale), the convergence of in some sense usually implies the...

This paper considers the problem of rate function identification for multidimensional queueing models with feedback. A set of techniques are introduced which allow this identification when the model possesses certain structural properties. The main tools used are representation formulas for...

Let {An n=1,2,...} and {Bn n=1,2,...} be sequences of random variables andYn=B1+A1B2+A1A2B3+...+A1...An-1Bn.Let M be a positive real number. Define the time of ruin by TM=inf{n YnM} (TM=+[infinity], if Yn[less-than-or-equals, slant]M for n=1,2,...). We are interested in the ruin probabilities...

We consider the filtering problem for a partially observable stochastic process , solution to a nonlinear system of stochastic difference equations, which provides a stochastic modellization for both the mean and the variance of the Gaussian observation distribution. The noises in the equations...

Ruin and related problems are studied for a risk business with compounding assets when the cash flow and the cumulative interest rate are diffusion processes with coefficients depending on the time and on the current cash balance. Differential equations are obtained for the probabilities of ruin...

We consider a reaction-diffusion equation in a bounded domain , driven by a space-time white noise, with a drift term having polynomial growth and a diffusion term which is not boundedly invertible, in general. We are showing that the transition semigroup corresponding to the equation has a...

Let be a non-separable Banach space of real-valued functions endowed with a weighted sup-norm. We consider partial sum processes as random functions with values in . We establish weak convergence statements for these processes via their weighted approximation in probability by an appropriate...