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 $α>1/2$ and show that only local properties of the covariance function play role for such results.

Published at http://dx.doi.org/10.3150/14-BEJ662 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)