On Convergence of the Uniform Norm and Approximation for Stochastic Processes from the Space $${\textbf{F}}_\psi (\Omega )$$

Abstract

In this paper, we consider random variables and stochastic processes from the space \({\textbf{F}}_\psi (\Omega )\) and study approximation problems for such processes. The method of series decomposition of a stochastic process from \({\textbf{F}}_\psi (\Omega )\) is used to find an approximating process called a model. The rate of convergence of the model to the process in the uniform norm is investigated. We develop an approach for estimating the cut-off level of the model under given accuracy and reliability of the simulation.