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On the Equivalence of Multiparameter Gaussian Processes

Author

Listed:
  • Tommi Sottinen

    (University of Helsinki)

  • Ciprian A. Tudor

    (Université de Paris 6)

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.

Suggested Citation

  • Tommi Sottinen & Ciprian A. Tudor, 2006. "On the Equivalence of Multiparameter Gaussian Processes," Journal of Theoretical Probability, Springer, vol. 19(2), pages 461-485, June.
    • Handle: RePEc:spr:jotpro:v:19:y:2006:i:2:d:10.1007_s10959-006-0022-5
    DOI: 10.1007/s10959-006-0022-5
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    References listed on IDEAS

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    1. T. Sottinen, 2004. "On Gaussian Processes Equivalent in Law to Fractional Brownian Motion," Journal of Theoretical Probability, Springer, vol. 17(2), pages 309-325, April.
    2. Baudoin, Fabrice & Nualart, David, 2003. "Equivalence of Volterra processes," Stochastic Processes and their Applications, Elsevier, vol. 107(2), pages 327-350, October.
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