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On the transition densities for reflected diffusions

Part of: Special processes Markov processes

Published online by Cambridge University Press:  01 July 2016

Vadim Linetsky
Vadim Linetsky*
Affiliation:
Northwestern University
*
∗ Postal address: Department of Industrial Engineering and Management Sciences, McCormick School of Engineering and Applied Sciences, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208, USA. Email address: linetsky@iems.northwestern.edu
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Abstract

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Diffusion models in economics, finance, queueing, mathematical biology, and electrical engineering often involve reflecting barriers. In this paper, we study the analytical representation of transition densities for reflected one-dimensional diffusions in terms of their associated Sturm-Liouville spectral expansions. In particular, we provide explicit analytical expressions for transition densities of Brownian motion with drift, the Ornstein-Uhlenbeck process, and affine (square-root) diffusion with one or two reflecting barriers. The results are easily implementable on a personal computer and should prove useful in applications.

Keywords

Reflected diffusionreflected Brownian motionreflected Ornstein-Uhlenbeck processreflected affine processspectral expansioncurrency target zoneheavy traffic

MSC classification

Primary: 60J35: Transition functions, generators and resolvents 60J60: Diffusion processes 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) 60K25: Queueing theory
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 37 , Issue 2 , June 2005 , pp. 435 - 460
Copyright
Copyright © Applied Probability Trust 2005 

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