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A strong uniform approximation of fractional Brownian motion by means of transport processes

Author

Listed:
  • Garzón, J.
  • Gorostiza, L.G.
  • León, J.A.

Abstract

We construct a sequence of processes that converges strongly to fractional Brownian motion uniformly on bounded intervals for any Hurst parameter H, and we derive a rate of convergence, which becomes better when H approaches 1/2. The construction is based on the Mandelbrot-van Ness stochastic integral representation of fractional Brownian motion and on a strong transport process approximation of Brownian motion. The objective of this method is to facilitate simulation.

Suggested Citation

  • Garzón, J. & Gorostiza, L.G. & León, J.A., 2009. "A strong uniform approximation of fractional Brownian motion by means of transport processes," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3435-3452, October.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:10:p:3435-3452
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    References listed on IDEAS

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    1. Szabados, Tamás, 2001. "Strong approximation of fractional Brownian motion by moving averages of simple random walks," Stochastic Processes and their Applications, Elsevier, vol. 92(1), pages 31-60, March.
    2. Enriquez, Nathanaël, 2004. "A simple construction of the fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 109(2), pages 203-223, February.
    3. Tommi Sottinen, 2001. "Fractional Brownian motion, random walks and binary market models," Finance and Stochastics, Springer, vol. 5(3), pages 343-355.
    4. Klüppelberg, Claudia & Kühn, Christoph, 2004. "Fractional Brownian motion as a weak limit of Poisson shot noise processes--with applications to finance," Stochastic Processes and their Applications, Elsevier, vol. 113(2), pages 333-351, October.
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    Cited by:

    1. Nguyen, Giang T. & Peralta, Oscar, 2020. "An explicit solution to the Skorokhod embedding problem for double exponential increments," Statistics & Probability Letters, Elsevier, vol. 165(C).

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