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Invariant Measures of Ultimately Bounded Stochastic Processes

Published online by Cambridge University Press:  22 January 2016

Yoshio Miyahara
Yoshio Miyahara*
Affiliation:
Nagoya University
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The author discussed in [4] the ultimate boundedness of a system which is governed by a stochastic differential equation

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 49 , March 1973 , pp. 149 - 153
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1973

References

[1] Benes, V. E.: Finite Regular Invariant Measures for Feller Process, J. Appl. Prob. 5 (1968), 203–209.Google Scholar
[2] Dynkin, E. B.: Markov Process, Springer-Verlag (1965).Google Scholar
[3] Khas’minskii, R. Z.: Ergodic Properties of Recurrent Diffusion Processes and Stabilizaztion of the Solution to the Cauchy Problem for Parabolic Equations, Theory Prob. Applications, Vol. 5, No. 2 (1960), 179–196.Google Scholar
[4] Miyahara, Y.: Ultimate Boundedness of the Systems Governed by Stochastic Differential Equations, to appear in Nagoya Math. J. Vol.47 (1972).Google Scholar
[5] Yosida, K.: Functional Analysis, Springer-Verlag (1965).Google Scholar
[6] Wonham, W. M.: Liapunov Criteria for Weak Stochastic Stabillity, J. Diff. Eq., Vol. 2 (1966), 195–207.Google Scholar
[7] Zakai, M.: A Liapunov Criterion for the Existence of Stationary Probability Distributions for Systems Perturbed by Noise, SIAM J. Control, Vol. 7, No. 3 (1969), 390–397.CrossRefGoogle Scholar