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The moments of the area under reflected Brownian bridge conditional on its local time at zero

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  • Frank B. Knight

Abstract

This paper develops a recursion formula for the conditional moments of the area under the absolute value of Brownian bridge given the local time at 0. The method of power series leads to a Hermite equation for the generating function of the coefficients which is solved in terms of the parabolic cylinder functions. By integrating out the local time variable, this leads to an integral expression for the joint moments of the areas under the positive and negative parts of the Brownian bridge.

Suggested Citation

  • Frank B. Knight, 2000. "The moments of the area under reflected Brownian bridge conditional on its local time at zero," International Journal of Stochastic Analysis, Hindawi, vol. 13, pages 1-26, January.
    • Handle: RePEc:hin:jnijsa:430231
    DOI: 10.1155/S1048953300000137
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    Cited by:

    1. Mario Abundo & Danilo Del Vescovo, 2017. "On the Joint Distribution of First-passage Time and First-passage Area of Drifted Brownian Motion," Methodology and Computing in Applied Probability, Springer, vol. 19(3), pages 985-996, September.
    2. Mario Abundo, 2013. "On the First-Passage Area of a One-Dimensional Jump-Diffusion Process," Methodology and Computing in Applied Probability, Springer, vol. 15(1), pages 85-103, March.
    3. Mario Abundo & Sara Furia, 2019. "Joint Distribution of First-Passage Time and First-Passage Area of Certain Lévy Processes," Methodology and Computing in Applied Probability, Springer, vol. 21(4), pages 1283-1302, December.

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