Stochastic Analysis of Gaussian Processes via Fredholm Representation. (31st July 2016) - Sottinen, Tommi; Viitasaari, Lauri
Abstract : 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. We show the convenience of the Fredholm representation by giving applications to equivalence in law, bridges, series expansions, stochastic differential equations, and maximum likelihood estimations.