On moments of Brownian functionals and their interpretation in terms of random walks

Joseph Najnudel, Ching-Tang Wu and Ju-Yi Yen

Statistics & Probability Letters, 2020, vol. 161, issue C

Abstract: An identity in law, shown in Mansuy and Yor (2008); Yor (1991), involves integrals of quadratic functionals of the Brownian motion. The corresponding equalities of moments bring in equalities of multiple integrals of joint moments of the Brownian motion taken at different times. In the present paper, we compute these moments, and deduce an interpretation of some of these computations in terms of combinatorial sums indexed by different paths of random walks.

Keywords: Brownian quadratic functionals; Distributional integration by parts (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1016/j.spl.2020.108724

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