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

Research output: Contribution to journalArticle (Academic Journal)peer-review

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 languageEnglish
Article number108724
JournalStatistics and Probability Letters
Volume161
Early online date12 Feb 2020
DOIs
Publication statusPublished - 1 Jun 2020

Keywords

  • Brownian quadratic functionals
  • Distributional integration by parts

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