Integral representation of random variables with respect to Gaussian processes

Abstract

It was shown in Mishura et al. (Stochastic Process. Appl. 123 (2013) 2353–2369), that any random variable can be represented as improper pathwise integral with respect to fractional Brownian motion. In this paper, we extend this result to cover a wide class of Gaussian processes. In particular, we consider a wide class of processes that are Hölder continuous of order $\alpha>1/2$ and show that only local properties of the covariance function play role for such results.