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2005 Exponential functionals of Brownian motion, II: Some related diffusion processes
Hiroyuki Matsumoto, Marc Yor
Probab. Surveys 2: 348-384 (2005). DOI: 10.1214/154957805100000168

Abstract

This is the second part of our survey on exponential functionals of Brownian motion. We focus on the applications of the results about 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.

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Hiroyuki Matsumoto. Marc Yor. "Exponential functionals of Brownian motion, II: Some related diffusion processes." Probab. Surveys 2 348 - 384, 2005. https://doi.org/10.1214/154957805100000168

Information

Published: 2005
First available in Project Euclid: 21 November 2005

zbMATH: 1189.91232
MathSciNet: MR2203676
Digital Object Identifier: 10.1214/154957805100000168

Subjects:
Primary: 60J65
Secondary: 60H30 , 60J60

Keywords: Brownian motion , heat kernel , Hyperbolic space , Lévy’s theorem , Pitman’s theorem , random environment

Rights: Copyright © 2005 The Institute of Mathematical Statistics and the Bernoulli Society

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