Sample Paths Properties of Stochastic Processes from Orlicz Spaces, with Applications to Partial Differential Equations

Abstract

In this paper we obtain conditions for stochastic processes from Orlicz spaces defined on unbounded domains to have almost sure bounded and continuous sample paths. Estimates for distributions of suprema of the processes are presented. Conditions are given in terms of entropy integrals and majorant characteristics of Orlicz spaces. Possible applications to solutions of partial differential equations are discussed. Examples of processes are given for which the conditions of the main results are satisfied.