On the Equivalence of Multiparameter Gaussian Processes

Tommi Sottinen () and Ciprian A. Tudor
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Tommi Sottinen: University of Helsinki
Ciprian A. Tudor: Université de Paris 6

Journal of Theoretical Probability, 2006, vol. 19, issue 2, 461-485

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.

Keywords: Brownian sheet; fractional Brownian sheet; equivalence of Gaussian processes; Hitsuda representation; Shepp representation; canonical representation of Gaussian processes; Girsanov theorem; stochastic differential equations; Primary 60G15; Secondary 60G30; Secondary 60H05 (search for similar items in EconPapers)
Date: 2006
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DOI: 10.1007/s10959-006-0022-5

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