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On the transition densities for reflected diffusions

  • Vadim Linetsky (a1)


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.

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Corresponding author

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:


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