Fredholm representation of multiparameter Gaussian processes with applications to equivalence in law and series expansions✩
Volume 2, Issue 3 (2015): PRESTO-2015, pp. 287–295
Pub. online: 2 October 2015
Type: Research Article
Open Access
Open Access
✩
The authors thank the referees for their useful comments.
1
Lauri Viitasaari was partially funded by Emil Aaltonen Foundation.
Received
25 June 2015
25 June 2015
Revised
21 September 2015
21 September 2015
Accepted
21 September 2015
21 September 2015
Published
2 October 2015
2 October 2015
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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