Trivariate distribution of sticky Brownian motion

In this short note we derive a closed form for the trivariate distribution (position, local time at the origin, and positive occupation time) of the one-dimensional sticky Brownian motion, thereby filling some gaps and fixing some mistakes in the literature.

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Publication Details

Journal
Journal of Mathematical Analysis and Applications
Published
2026-02-19
DOI
https://doi.org/10.1016/j.jmaa.2026.130544
Primary Topic
Random Matrices and Applications
Type
article
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article

Trivariate distribution of sticky Brownian motion

Jean-Baptiste Casteras, Léonard Monsaingeon
Journal of Mathematical Analysis and Applications
Random Matrices and Applications
article

Trivariate distribution of sticky Brownian motion

Jean-Baptiste Casteras, Léonard Monsaingeon
article en

Abstract

In this short note we derive a closed form for the trivariate distribution (position, local time at the origin, and positive occupation time) of the one-dimensional sticky Brownian motion, thereby filling some gaps and fixing some mistakes in the literature.

Journal of Mathematical Analysis and ApplicationsVol. 560(2)
University of Lisbon (PT), Institut Élie Cartan de Lorraine (FR), Instituto Superior Técnico (PT), Universidade Nova de Lisboa (PT)
Reduced inequalities
Openalex Percentile: Top 53%
Random Matrices and Applications
DOIOpen Access PDFOpenAlex
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