Dual representations of Laplace transforms of Brownian excursion and generalized meanders

Włodzimierz Bryc; Yizao Wang

doi:10.1016/j.spl.2018.04.021

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arXiv · 1706.01578

Dual representations of Laplace transforms of Brownian excursion and generalized meanders

Włodzimierz Bryc·Yizao Wang

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Abstract

The Laplace transform of the $d$-dimensional distribution of Brownian excursion is expressed as the Laplace transform of the $(d+1)$-dimensional distribution of an auxiliary Markov process, started from a $\sigma$-finite measure and with the roles of arguments and times interchanged. A similar identity holds for the Laplace transform of a generalized meander, which is expressed as the Laplace transform of the same auxiliary Markov process, with a different initial law.

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Włodzimierz Bryc, Yizao Wang. 2017-06-06. Dual representations of Laplace transforms of Brownian excursion and generalized meanders. https://doi.org/10.1016/j.spl.2018.04.021

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