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On Gaussian Processes Equivalent in Law to Fractional Brownian Motion

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  • T. Sottinen

    (University of Helsinki)

Abstract

We consider Gaussian processes that are equivalent in law to the fractional Brownian motion and their canonical representations. We prove a Hitsuda type representation theorem for the fractional Brownian motion with Hurst index H≤1/2. For the case H>1/2 we show that such a representation cannot hold. We also consider briefly the connection between Hitsuda and Girsanov representations. Using the Hitsuda representation we consider a certain special kind of Gaussian stochastic equation with fractional Brownian motion as noise.

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  • 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.
    • Handle: RePEc:spr:jotpro:v:17:y:2004:i:2:d:10.1023_b:jotp.0000020696.99064.5d
    DOI: 10.1023/B:JOTP.0000020696.99064.5d
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    References listed on IDEAS

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    1. 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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    Cited by:

    1. 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.

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