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Bounds for the Mixing Rate in the Theory of Stochastic Equations
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1988
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Large DeviationsEngineeringEntropyDiffusion ProcessesStochastic ProcessesStochastic SystemStochastic CalculusMixing RateStochastic EquationsStochastic Dynamical SystemStochastic AnalysisProbability TheoryStochastic PhenomenonStochastic Differential EquationStatisticsGoogle Scholar
Previous article Next article Bounds for the Mixing Rate in the Theory of Stochastic EquationsA. Yu. VeretennikovA. Yu. Veretennikovhttps://doi.org/10.1137/1132036PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] I. A. Ibragimov and , Yu. V. Linnik, Independent and stationary sequences of random variables, Wolters-Noordhoff Publishing, Groningen, 1971, 443– 48:1287 0219.60027 Google Scholar[2] A. D. Vent-tsel' and , M. I. Friedlin, Fluctuations in Dynamical Systems under the Action of Small Random Perturbations, Nauka, Moscow, 1979, (In Russian.) 0499.60053 Google Scholar[3] V. A. Statulyvaichus, Large deviation theorems for sums of dependent random variables. I, Litovsk. Mat. Sb., 19 (1979), 199–208, 214–215, (In Russian.) 81i:60028 Google Scholar[4] Yu. A. Davydov, Mixing conditions for Markov chains, Theory Probab. Appl., 18 (1973), 312–329 10.1137/1118033 0297.60031 LinkGoogle Scholar[5] N. V. Krylov, On Itô stochastic integral equations, Theory Probab. Appl., 14 (1969), 330–336 10.1137/1114042 0281.60066 LinkGoogle Scholar[6] N. V. Krylov, The selection of a Markov process from a Markov system of processes, and the construction of quasidiffusion processes, Izv. Akad. Nauk SSSR Ser. Mat., 37 (1973), 691–708, (In Russian.) 49:4097 0295.60057 Google Scholar[7] N. V. Krylov, N. V. Krylov, Once more about the connection between elliptic operators and Itô's stochastic equationsStatistics and control of stochastic processes (Moscow, 1984), Transl. Ser. Math. Engrg., Optimization Software, New York, 1985, 214–229, Steklov seminar 87j:60088 0568.60060 Google Scholar[8] E. B. Dynkin, Markov Processes, Academic Press, New York, 1965 0132.37901 CrossrefGoogle Scholar[9] H. P. McKean, Stochastic integrals, Probability and Mathematical Statistics, No. 5, Academic Press, New York, 1969xiii+140 40:947 0191.46603 Google Scholar[10] David Griffeath, A maximal coupling for Markov chains, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 31 (1974/75), 95–106 51:6996 0301.60043 CrossrefGoogle Scholar[11] D. Stroock and , S. R. S. Varadhan, On the support of diffusion processes with applications to the strong maximum principle, Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability (Univ. California, Berkeley, Calif., 1970/1971), Vol. III: Probability theory, Univ. California Press, Berkeley, Calif., 1972, 333–359 53:4259 0255.60056 Google Scholar[12] N. V. Krylov and , M. V. Safonov, A certain property of the solutions of parabolic equations with measurable coefficients, Izv. Akad. Nauk SSSR, 44 (1980), 161–175, (In Russian.) Google Scholar[13] D. Stroock and , S. R. S. Varadhan, Multidimensional diffusion processes, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], Vol. 233, Springer-Verlag, Berlin, 1979xii+338 81f:60108 0426.60069 Google Scholar[14] J. L. 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