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On the transition densities for reflected diffusions

Published online by Cambridge University Press:  01 July 2016

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: [email protected]
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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.

Type
General Applied Probability
Copyright
Copyright © Applied Probability Trust 2005 

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