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Journal of Theoretical Probability

, Volume 19, Issue 2, pp 461–485 | Cite as

On the Equivalence of Multiparameter Gaussian Processes

  • Tommi Sottinen
  • Ciprian A. Tudor
Article

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 

Mathematics Subject Classification (2000)

Primary 60G15 Secondary 60G30 Secondary 60H05 

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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of HelsinkiHelsinkiFinland
  2. 2.Laboratoire de ProbabilitésUniversité de Paris 6ParisFrance

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