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

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

2005-11-21

arxiv.org/abs/math/0511519v2

Probability Surveys 2005, Vol. 2, 348-384

Mathematics

Probability

Published at http://dx.doi.org/10.1214/154957805100000168 in the Probability Surveys (http://www.i-journals.org/ps/) by the In

Scientific paper

10.1214/154957805100000168

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 L\'{e}vy's and Pitman's theorems are discussed.

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