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A frequency domain approach to some results on fractional Brownian motion

Author

Listed:
  • Dzhaparidze, K.
  • Ferreira, J. A.

Abstract

Let X be a fractional Brownian motion. It is known that Mt=[integral operator]mt dX, t[greater-or-equal, slanted]0, where mt is a certain kernel, defines a martingale M, and also that X can be represented by Xt=[integral operator]xt dM, t[greater-or-equal, slanted]0, for some kernel xt. We derive these results by using the spectral representation of the covariance function of X. A formula for the covariance between X and M is also given.

Suggested Citation

  • Dzhaparidze, K. & Ferreira, J. A., 2002. "A frequency domain approach to some results on fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 60(2), pages 155-168, November.
    • Handle: RePEc:eee:stapro:v:60:y:2002:i:2:p:155-168
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    Cited by:

    1. Dzhaparidze, Kacha & van Zanten, Harry & Zareba, Pawel, 2005. "Representations of fractional Brownian motion using vibrating strings," Stochastic Processes and their Applications, Elsevier, vol. 115(12), pages 1928-1953, December.

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