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

Joseph Najnudel; Ching Tang Wu; Ju Yi Yen

doi:10.1016/j.spl.2020.108724

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

Joseph Najnudel, Ching Tang Wu^*, Ju Yi Yen^*

^*Corresponding author for this work

School of Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

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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.

Original language	English
Article number	108724
Journal	Statistics and Probability Letters
Volume	161
Early online date	12 Feb 2020
DOIs	https://doi.org/10.1016/j.spl.2020.108724
Publication status	Published - 1 Jun 2020

Keywords

Brownian quadratic functionals
Distributional integration by parts

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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.",

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AU - Wu, Ching Tang

AU - Yen, Ju Yi

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Y1 - 2020/6/1

N2 - 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.

AB - 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.

KW - Brownian quadratic functionals

KW - Distributional integration by parts

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DO - 10.1016/j.spl.2020.108724

M3 - Article (Academic Journal)

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JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

SN - 0167-7152

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ER -

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

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