Open Access
2024 A new three-dimensional extension of Bougerol’s identity in law
Kolitha Perera
Author Affiliations +
Electron. Commun. Probab. 29: 1-7 (2024). DOI: 10.1214/24-ECP577


Bougerol’s identity in law is one of the most infamous in the study of Brownian motion. To that end, in this paper, we present a further extension of its study through a proof in the third dimension. Second-dimension proofs have been extensively explored, as have those of the third dimension. However, here we will extrapolate a previously two-dimensional proof into the third dimension through the use of a three-Brownian joint distribution.


The author is grateful to the editor for taking the time to read his work.


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Kolitha Perera. "A new three-dimensional extension of Bougerol’s identity in law." Electron. Commun. Probab. 29 1 - 7, 2024.


Received: 8 August 2023; Accepted: 11 February 2024; Published: 2024
First available in Project Euclid: 22 February 2024

Digital Object Identifier: 10.1214/24-ECP577

Primary: 60J65
Secondary: 60H15

Keywords: Bougerol’s identity , Brownian motion , Stochastic partial differential equations , stochastics

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