On Moduli of Continuity for Gaussian and l2-Norm Squared Processes Generated by Ornstein-Uhlenbeck Processes

Abstract

Let be a sequence of independent Ornstein-Uhlenbeck processes with coefficients lk and ƛk,i.e., Xk(.)is a Gaussian process with EXk(t) =0 andThe process Y(.)was first studied by Dawson (1972) as the stationary solution of the infinite array of stochastic differential equationswhere are independent Wiener processes (cf. also [6],[19],and [1]).