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 Probability Surveys > Vol. 2 (2005) open journal systems 

Exponential functionals of Brownian motion, II: Some related diffusion processes

Hiroyuki Matsumoto, Graduate School of Information Science, Nagoya University
Marc Yor, Laboratoire de Probabilite, Universite Pierre et Marie Curie

This is the second part of our survey on exponential functionals of Brownian motion. We focus on the applications of the results on the distributions of the exponential functionals, which have been discussed in the first part. Pricing formula for call options for the Asian options, explicit expressions for the heat kernels on hyperbolic spaces, diffusion processes in random environments and extensions of Lévy's and Pitman's theorems are discussed.

AMS 2000 subject classifications: Primary 60J65; secondary 60J60, 60H30.

Keywords: Brownian motion, hyperbolic space, heat kernel, random environment, Lévy's theorem, Pitman's theorem.

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Matsumoto, Hiroyuki, Yor, Marc, Exponential functionals of Brownian motion, II: Some related diffusion processes, Probability Surveys, 2, (2005), 348-384 (electronic).


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