Hostname: page-component-848d4c4894-pjpqr Total loading time: 0 Render date: 2024-06-25T00:30:43.432Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Ethier, S. N. and Kurtz, T. G. (1986) Markov Processes, Characterization and Convergence. Wiley, New York.CrossRefGoogle Scholar
[2] Feller, W. (1966) An Introduction to Probability Theory and its Applications, Vol. II. Wiley, New York.Google Scholar
[3] Gihman, I. I, and Skorohod, A. V. (1972) Stochastic Differential Equations. Springer-Verlag, Berlin.CrossRefGoogle Scholar
[4] Giorno, V., Nobile, A. G. and Ricciardi, L. M. (1989) A symmetry-based constructive approach to probability densities for one-dimensional diffusion processes. J. Appl. Prob. 27, 707–721.Google Scholar
[5] Ikeda, N. and Watanabe, S. (1981) Stochastic Differential Equations and Diffusion Processes. North-Holland, Amsterdam.Google Scholar
[6] Nobile, A. G. and Ricciardi, L. M. (1984) Growth with regulation in fluctuating environments. I. Alternative logistic like diffusion models. Biol. Cybernet. 49, 179–188.Google Scholar
[7] Nobile, A. G. and Ricciardi, L. M. (1984) Growth with regulation in fluctuating environments. II. Intrinsic lower bounds to population size. Biol. Cybernet. 50, 285–299.Google Scholar