Dual representations of Laplace transforms of Brownian excursion and generalized meanders

Włodzimierz Bryc and Yizao Wang

Statistics & Probability Letters, 2018, vol. 140, issue C, 77-83

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 σ-finite measure and with the roles of arguments and times interchanged. A similar identity holds for the Laplace transform of a generalized Brownian meander, which is expressed as the Laplace transform of the same auxiliary Markov process, with a different initial law.

Keywords: Brownian excursion; Brownian meander; Laplace transform; Markov process (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1016/j.spl.2018.04.021

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