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 Probability Surveys > Vol. 9 (2012) open journal systems 

Bougerol's identity in law and extensions

Stavros Vakeroudis

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.

AMS 2000 subject classifications: Primary 60J65, 60J60, 60-02, 60G07; secondary 60G15, 60J25, 60G46, 60E10, 60J55, 30C80, 44A10.

Keywords: 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.

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Vakeroudis, Stavros, Bougerol's identity in law and extensions, Probability Surveys, 9, (2012), 411-437 (electronic). DOI: 10.1214/12-PS195.


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