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Transition probability density of a certain diffusion process concentrated on a finite spatial interval

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

A. Milian
A. Milian*
Affiliation:
Technical University of Cracow
*
∗Postal address: Institute of Mathematics, Technical University of Cracow, ul. Warszawska 24, 31–155 Kraków, Poland.
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Abstract

We show that under some assumptions a diffusion process satisfying a one-dimensional Itô's equation has a transition probability density concentrated on a finite spatial interval. We give a formula for this density.

Keywords

ONE-DIMENSIONAL DIFFUSIONS SATISFYING ITÔ'S EQUATIONTIME-DEPENDENTBOUNDARIESTRANSITION PROBABILITY DENSITY

MSC classification

Primary: 60J60: Diffusion processes
Secondary: 60J35: Transition functions, generators and resolvents 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 29 , Issue 2 , June 1992 , pp. 334 - 342
Copyright
Copyright © Applied Probability Trust 1992 

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References

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