On the transition densities for reflected diffusions

Vadim Linetsky*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

84 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)435-460
Number of pages26
JournalAdvances in Applied Probability
Issue number2
StatePublished - Jun 2005


  • Currency target zone
  • Heavy traffic
  • Reflected Brownian motion
  • Reflected Ornstein-Uhlenbeck process
  • Reflected affine process
  • Reflected diffusion
  • Spectral expansion

ASJC Scopus subject areas

  • Statistics and Probability
  • Applied Mathematics


Dive into the research topics of 'On the transition densities for reflected diffusions'. Together they form a unique fingerprint.

Cite this