Exponential functionals of Brownian motion and disordered systems
Alain Comtet (DPT, IPN Orsay France) C\'ecile Monthus (SPhT, CE Saclay, France), Marc Yor (Labo. Proba., Paris France)
TL;DR
This paper investigates exponential functionals of Brownian motion, exploring their properties and distributions in contexts like finance and disordered systems, with explicit results for free energy distributions in particle models.
Contribution
It provides new explicit expressions for the distribution of exponential functionals related to Brownian motion in disordered systems.
Findings
Explicit distribution formulas for free energy in Wiener potential models
Connections between exponential functionals and disordered system behaviors
Enhanced understanding of Brownian motion in complex environments
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.
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Taxonomy
Topicsstochastic dynamics and bifurcation · Stochastic processes and statistical mechanics · Stochastic processes and financial applications