On the transition densities for reflected diffusions
- 1 June 2005
- journal article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 37 (2), 435-460
- https://doi.org/10.1239/aap/1118858633
Abstract
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
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