The question of completeness of the spectral domain generated by a bimeasure is discussed. The bimeasure is derived from a spectral representation of a given process of weak class (C). In particular by an example it is shown that the spectral domain of a weak class (C) process is not necessarily...

We construct a.s. nonlinear regression representations of general stochastic processes . As a consequence we obtain in particular special regression representations of Markov chains and of certain m-dependent sequences. For m-dependent sequences we obtain a constructive method to check, whether...

We consider optimal stopping of independent sequences. Assuming that the corresponding imbedded planar point processes converge to a Poisson process we introduce some additional conditions which allow to approximate the optimal stopping problem of the discrete time sequence by the optimal...

For a class of point processes including nonhomogeneous Poisson processes, some Cox processes and some processes of non-Poisson type, the question of existence and construction of complete and sufficient statistics is investigated. The results are based on the generalization of some results from...

In proving limit theorems for some stochastic processes, the following classes of distribution functions were introduced by Chover--Ney--Wainger and Chistyakov F belongs to ([lambda]) if and only if: 1. (i) 2. (ii) for all yreal, 3. (iii)[integral operator][infinity]0...

Distributions of sample quantiles of measurable stochastic processes are important for the purpose of rational pricing of "look-back" options. In this paper we compute the exact tail behavior of the sample quantile distribution for a large class of infinitely divisible stochastic processes with...