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Exponential functionals of Brownian motion and disordered systems

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

Alain Comtet ,
Cécile Monthus  and
Marc Yor
Alain Comtet*
Affiliation:
IPN
Cécile Monthus*
Affiliation:
C.E. Saclay
Marc Yor*
Affiliation:
Université Paris 6
*
∗Postal address: (1) Division de Physique Théorique (Unité de Recherche des Universités Paris 6 et Paris 11 associée au CNRS), IPN Bâtiment 100, 91406 Orsay Cédex; (2) L.P.T.P.E., Tour 12, 4 Place Jussieu 75252 Paris Cedex 05, France. E-mail address: [email protected]
∗∗Postal address: Service de Physique Théorique, C. E. Saclay, Orme des Merisiers, 91191 Gif-sur-Yvette Cédex, France. E-mail address: [email protected]
∗∗∗Postal address: Laboratoire de Probabilités, Université Paris 6, 4 Place Jussieu, Tour 56, 75252 Paris Cedex 05, France.
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Abstract

The paper deals with exponential functionals of the linear Brownian motion which arise in different contexts, such as continuous time finance models and one-dimensional disordered models. We study some properties of these exponential functionals in relation with the problem of a particle coupled to a heat bath in a Wiener potential. Explicit expressions for the distribution of the free energy are presented.

Keywords

Exponentials of Brownian motiondisordered systemspartition functionfree energy

MSC classification

Primary: 60J65: Brownian motion
Type
Research Papers
Information
Journal of Applied Probability , Volume 35 , Issue 2 , June 1998 , pp. 255 - 271
Copyright
Copyright © Applied Probability Trust 1998 

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