On the Equivalence of Multiparameter Gaussian Processes |
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| Authors: | Tommi Sottinen Ciprian A Tudor |
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| Institution: | (1) Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, 00014 Helsinki, Finland;(2) Laboratoire de Probabilités, Université de Paris 6, 4, place Jussieu, 75252 Paris, France |
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| Abstract: | Our purpose is to characterize the multiparameter Gaussian processes, that is Gaussian sheets, that are equivalent in law
to the Brownian sheet and to the fractional Brownian sheet. We survey multiparameter analogues of the Hitsuda, Girsanov and
Shepp representations. As an application, we study a special type of stochastic equation with linear noise.
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| Keywords: | Brownian sheet fractional Brownian sheet equivalence of Gaussian processes Hitsuda representation Shepp representation canonical representation of Gaussian processes Girsanov theorem stochastic differential equations |
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