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Decomposing the Brownian path via the range process

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  • Vallois, P.

Abstract

We decompose the Brownian trajectory from extremes, via the inverse of the range process. This allows us to construct a martingale which satisfies the chaotic property representation and is closely connected to parabolic martingale.

Suggested Citation

  • Vallois, P., 1995. "Decomposing the Brownian path via the range process," Stochastic Processes and their Applications, Elsevier, vol. 55(2), pages 211-226, February.
    • Handle: RePEc:eee:spapps:v:55:y:1995:i:2:p:211-226
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    References listed on IDEAS

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    1. Imhof, J. P., 1992. "A construction of the brownian path from BES3 pieces," Stochastic Processes and their Applications, Elsevier, vol. 43(2), pages 345-353, December.
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    Cited by:

    1. Etienne Tanré & Pierre Vallois, 2006. "Range of Brownian Motion with Drift," Journal of Theoretical Probability, Springer, vol. 19(1), pages 45-69, January.
    2. Russo, Francesco & Vallois, Pierre, 1998. "Product of two multiple stochastic integrals with respect to a normal martingale," Stochastic Processes and their Applications, Elsevier, vol. 73(1), pages 47-68, January.

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    1. Etienne Tanré & Pierre Vallois, 2006. "Range of Brownian Motion with Drift," Journal of Theoretical Probability, Springer, vol. 19(1), pages 45-69, January.

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