Probability Surveys

Bougerol’s identity in law and extensions

Stavros Vakeroudis

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We present a list of equivalent expressions and extensions of Bougerol’s celebrated identity in law, obtained by several authors. We recall well-known results and the latest progress of the research associated with this celebrated identity in many directions, we give some new results and possible extensions and we try to point out open questions.

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Probab. Surveys, Volume 9 (2012), 411-437.

First available in Project Euclid: 8 November 2012

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Primary: 60J65: Brownian motion [See also 58J65] 60J60: Diffusion processes [See also 58J65] 60-02: Research exposition (monographs, survey articles) 60G07: General theory of processes
Secondary: 60G15: Gaussian processes 60J25: Continuous-time Markov processes on general state spaces 60G46: Martingales and classical analysis 60E10: Characteristic functions; other transforms 60J55: Local time and additive functionals 30C80: Maximum principle; Schwarz's lemma, Lindelöf principle, analogues and generalizations; subordination 44A10: Laplace transform

Bougerol’s identity time-change hyperbolic Brownian motion subordination Gauss-Laplace transform planar Brownian motion Ornstein-Uhlenbeck processes two-dimensional Bougerol’s identity local time multi-dimensional Bougerol’s identity Bougerol’s diffusion peacock convex order Bougerol’s process


Vakeroudis, Stavros. Bougerol’s identity in law and extensions. Probab. Surveys 9 (2012), 411--437. doi:10.1214/12-PS195.

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