Fredholm representation of multiparameter Gaussian processes with applications to equivalence in law and series expansions

Tommi Sottinen; Lauri Viitasaari

doi:10.15559/15-vmsta39cnf

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arXiv · 1506.07211

Fredholm representation of multiparameter Gaussian processes with applications to equivalence in law and series expansions

Tommi Sottinen·Lauri Viitasaari

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Abstract

We show that every multiparameter Gaussian process with integrable variance function admits a Wiener integral representation of Fredholm type with respect to the Brownian sheet. The Fredholm kernel in the representation can be constructed as the unique symmetric square root of the covariance. We analyze the equivalence of multiparameter Gaussian processes by using the Fredholm representation and show how to construct series expansions for multiparameter Gaussian processes by using the Fredholm kernel.

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BibTeX RIS

Tommi Sottinen, Lauri Viitasaari. 2015-06-23. Fredholm representation of multiparameter Gaussian processes with applications to equivalence in law and series expansions. https://doi.org/10.15559/15-vmsta39cnf

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