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Rates of convergence to the stationary distribution for k-dimensional diffusion processes

Published online by Cambridge University Press:  14 July 2016

P. L. Davies*
Affiliation:
Universität–GHS Essen
*
Postal address: Universität–GHS–Essen, Fachbereich 6, Mathematik, D-4300 Essen, W. Germany.

Abstract

Using a coupling technique, rates of convergence in total variation of certain k -dimensional diffusion processes to the stationary distribution are obtained. The results place assumptions only on the coefficients of the elliptic differential operator governing the diffusion.

Type
Research Paper
Copyright
Copyright © Applied Probability Trust 1986 

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References

[1] Bhattacharya, R. N. (1978) Criteria for recurrence and existence of invariant measures for multidimensional diffusions. Ann. Prob. 6, 541553; Correction 8 (1980), 1194–1195.CrossRefGoogle Scholar
[2] Florian, H.-J. (1984) Adiabatische Elimination bei Diffusionsprozessen. Dissertation, Universität–Gesamthochschule Essen.Google Scholar
[3] Friedman, A. (1975) Stochastic Differential Equations and Applications, Vol. 1. Academic Press, New York.Google Scholar
[4] Khas'minskii, R. Z. (1960) Ergodic properties of recurrent diffusion processes and stabilization of the solution to the Cauchy problem for parabolic equations. Theory Prob. Appl. V, 179196.Google Scholar
[5] Ladyzenskaja, O. A., Solonnikov, V. A. and Ural'Ceva, N. N. (1968) Linear and Quasilinear Equations of Parabolic Type. Translations of Mathematical Monographs 23, American Mathematical Society, Providence, RI.CrossRefGoogle Scholar
[6] Lindvall, T. (1982) On coupling of continuous-time renewal processes. J. Appl. Prob. 19, 8289.CrossRefGoogle Scholar
[7] Lindvall, T. (1983) On coupling of diffusion processes. J. Appl. Prob. 20, 8293.Google Scholar
[8] Papanicolaou, G. C., Stroock, D. W. and Varadhan, S. R. S. (1977) Martingale approach to some limit theorems. In 1976 Duke Turbulence Conference, Duke University Mathematics Series III, Mathematics Department, Duke University.Google Scholar
[9] Stroock, D. W. and Varadhan, S. R. S. (1970) On the support of diffusion processes with applications to the strong maximum principle. Proc. 6th Berkeley Symp. Math. Statist. Prob. 3, 333360.Google Scholar
[10] Stroock, D. W. and Varadhan, S. R. S. (1979) Multidimensional Diffusion Processes. Springer-Verlag, Berlin.Google Scholar