%0 Journal Article
%T Stochastic Analysis of Gaussian Processes via Fredholm Representation
%A Tommi Sottinen
%A Lauri Viitasaari
%J Mathematics
%D 2014
%I arXiv
%X We show that every separable Gaussian process with integrable variance function admits a Fredholm representation with respect to a Brownian motion. We extend the Fredholm representation to a transfer principle and develop stochastic analysis by using it. In particular, we prove an It\^o formula that is, as far as we know, the most general Malliavin-type It\^o formula for Gaussian processes so far. Finally, we give applications to equivalence in law and series expansions of Gaussian processes.
%U http://arxiv.org/abs/1410.2230v4