Hostname: page-component-848d4c4894-89wxm Total loading time: 0 Render date: 2024-07-05T21:46:30.919Z Has data issue: false hasContentIssue false
  • English
  • Français

On coupling of diffusion processes

Published online by Cambridge University Press:  14 July 2016

Torgny Lindvall
Torgny Lindvall*
Affiliation:
University of Göteborg
*
∗ Postal address: Department of Mathematics, University of Göteborg, 412 96 Göteborg, Sweden.
Get access Rights & Permissions [Opens in a new window]

Abstract

The coupling method is well fitted to be used in the study of the asymptotics of one-dimensional diffusion processes. We give an elementary proof of Orey's theorem in the recurrent case, and establish rate results for tendency towards equilibrium under moment conditions on the speed measure and the initial distributions.

Keywords

DIFFUSIONSCOUPLINGSERGODIC THEOREMRATE RESULTS
Type
Research Papers
Information
Journal of Applied Probability , Volume 20 , Issue 1 , March 1983 , pp. 82 - 93
Copyright
Copyright © Applied Probability Trust 1983 

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] Breiman, L. (1968) Probability. Addison-Wesley, Reading, MA.Google Scholar
[2] Freedman, D. (1971) Brownian Motion and Diffusion. Holden-Day, San Francisco.Google Scholar
[3] Fristedt, B. and Orey, S. (1978) The tail s-field of one-dimensional diffusions. In Stochastic Analysis, Academic Press, New York, 127–138.Google Scholar
[4] Gichman, I. I. and Skorochod, A. W. (1971) Stochastische Differentialgleichungen. Akademie-Verlag, Berlin.Google Scholar
[5] Griffeath, D. (1978) Coupling methods for Markov processes. In Advances in Mathematics Supplementary Studies 2: Studies in Probability and Ergodic Theory, 1–43.Google Scholar
[6] Küchler, U. and Lunze, U. (1980) On the tail s-field and the minimal parabolic functions for one-dimensional quasi-diffusions. Z. Wahrscheinlichkeitsth. 51, 303–322.Google Scholar
[7] Lindvall, T. (1979) A note on coupling of birth and death processes. J. Appl. Prob 16 505–512.CrossRefGoogle Scholar
[8] Mandl, P. (1968) Analytical Treatment of One-Dimensional Markov Processes. Springer-Verlag, Berlin.Google Scholar
[9] Pitman, J. W. (1974) Uniform rates of convergence for Markov chain transition probabilities. Z. Wahrscheinlichkeitsth. 29, 193–227.CrossRefGoogle Scholar
[10] Rösler, U. (1979) The tail s-field of time-homogeneous one-dimensional diffusion processes. Ann. Prob. 7, 847–857.Google Scholar
[11] Watanabe, H. and Motoo, M. (1958) Ergodic property of recurrent diffusion processes. J. Math. Soc. Japan 10, 271–286.Google Scholar