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Bougerol’s identity in law and extensions. (English) Zbl 1278.60125
Summary: 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.

60J65 Brownian motion
60J60 Diffusion processes
60-02 Research exposition (monographs, survey articles) pertaining to probability theory
60G07 General theory of stochastic processes
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
Full Text: DOI Euclid
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