Journal of Theoretical Probability

, Volume 17, Issue 2, pp 309–325 | Cite as

On Gaussian Processes Equivalent in Law to Fractional Brownian Motion

  • T. Sottinen


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.

Fractional Brownian motion equivalence of Gaussian processes Hitsuda representation canonical representation of Gaussian processes Girsanov theorem stochastic differential equations 


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Copyright information

© Plenum Publishing Corporation 2004

Authors and Affiliations

  • T. Sottinen
    • 1
  1. 1.Department of MathematicsUniversity of HelsinkiFinland

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