Bougerol's identity in law and extensions

Stavros Vakeroudis (1, 2)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 School of Mathematics - Department of Mathematics [Manchester]

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.

Mots clés: Bougerol's process; 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.

Domaines: Probabilités [math.PR]

Stavros Vakeroudis. Bougerol's identity in law and extensions. 2012. ⟨hal-00663488v1⟩