On local continuity moduli for Gaussian processes

Abstract

In this paper, we get three local continuity moduli theorems for the almost surely continuous, stationary increments Gaussian process {Y(t),t≥0}, the partial sum processesX(t,N)=Σ =1/ X k(t) of infinite dimensional Ornstein-Uhlenbeck processes {X k(t),t≥0} =1/∞ andl p-valued Gaussian processes {Y(t),t≥0}={X k(t),t≥0} =1/∞ separately. The first theorem implies the local continuity modulus theorem for the seriesX(t)=Σ =1/∞ X k(t) of infinite dimensional Ornstein-Uhlenbeck processes which has been obtained in [3].