This paper gives an upper bound for a Wasserstein distance between the distributions of a partial sum process of a Markov chain and a Poisson process on the positive half line in terms of the transition probabilities and the stationary distribution of the Markov chain. The argument is based on...

In this paper we introduce a new method for the problem of testing for randomness against the alternative of ARMA dependence. We give the asymptotic law of our statistic under the null hypothesis and under the alternative hypothesis. Our method is based on a new measure of information between...

This paper is devoted to the study of central limit theorems and the domain of normal attraction for some random processes with sample paths in exponential Orlicz spaces under metric entropy conditions. In particular, the local times of strongly symmetric standard Markov processes and random...

In this paper, we study the asymptotic distribution of a recursively defined stochastic process where are d-dimensional random vectors, b, d -- d and [sigma]: d -- d x r are locally Lipshitz continuous functions, {[var epsilon]n} are r-dimensional martingale differences, and {an} is a sequence...

Let Z(n), N = 0, 1, 2, ... be a critical branching process in random environment and Z(m, n), m <= n, the corresponding reduced process. We consider the case when the offspring generating functions are fractional linear and show that for any fixed m the conditional distribution of Z(m, n) given Z(n) > 0 converges to a non-trivial limit as n -- [infinity]. We also prove the convergence of the conditional distribution of the process {n-1/2 log Z([nt], n), 0 <= t <= 1} given Z(n) > 0 to the law of a transformation of the...</=></=>

A detailed estimate on the growth of the position coordinate in a nonlinearly perturbed Ornstein-Uhlenbeck phase process is given in all dimensions d = 3. The corresponding stochastic wave operators are constructed. A corresponding asymptotics of the phase space process for stochastically...

We discuss three forms of convergence in distribution which are stronger than the normal weak convergence, and are non-topological in nature. We give Storokhod representation results for two of these modes of convergence, and give applications to sufficient statistics and conditioned Markov...

A well-known property of stationary Gaussian processes is that the excursions over high levels ("peaks") have a limiting parabolic shape, each determined by a single random parameter. This means, in particular, that (in the limit) the length of a single excursion above a high level determines...

We propose a new method to get the Hermite polynomial expansion of crossings of any level by a stationary Gaussian process, as well as the one of the number of maxima in an interval, under some assumptions on the spectral moments of the process.

Polynomial bounds for the coefficient of [beta]-mixing are established for diffusion processes under weak recurrency assumptions. The method is based on direct evaluations of the moments and certain functionals of hitting-times of the process and on the change of time.