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• W2052512227 abstract "Previous article Next article On Subexponential Mixing Rate for Markov ProcessesS. A. Klokov and A. Yu. VeretennikovS. A. Klokov and A. Yu. Veretennikovhttps://doi.org/10.1137/S0040585X97980841PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractThis paper establishes subexponential bounds for the $beta$-mixing and the rate of convergence to invariant measure for homogeneous Markov processes with continuous and discrete time.[1] H. Ganidis, , B. Roynette and , and F. Simonot, Convergence rate of some semi‐groups to their invariant probability, Stochastic Process. Appl., 79 (1999), pp. 243–263. a2m STOPB7 0304-4149 Stochastic Proc. Appl. CrossrefGoogle Scholar[2] A. Guillin, Moderate deviations of inhomogeneous functionals of Markov processes and application to averaging, Stochastic Process. Appl., 92 (2001), pp. 287–313. a2m STOPB7 0304-4149 Stochastic Proc. Appl. CrossrefGoogle Scholar[3] Google Scholar[4] V. V. Kalashnikov, The property of γ‐reflexivity for Markov sequences, Sov. Math. Dokl., 14 (1973), pp. 1869–1873. a2f ZZZZZZ 0197-6788 Sov. Math. Dokl. Google Scholar[5] Google Scholar[6] Google Scholar[7] N. V. Krylov and and M. V. Safonov, A property of the solutions of parabolic equations with measurable coefficients, Izv. Akad. Nauk SSSR Ser. Mat., 44 (1980), pp. 161–175. b2y ZZZZZZ 0373-2436 Izv. Akad. Nauk SSSR, Ser. Mat. Google Scholar[8] Google Scholar[9] J. Lamperti, Criteria for stochastic processes. II. Passage‐time moments, J. Math. Anal. Appl., 7 (1963), pp. 127–145. jma JMANAK 0022-247X J. Math. Anal. Appl. CrossrefGoogle Scholar[10] M. N. Malyshkin, Subexponential estimates of the rate of convergence to the invariant measure for stochastic differential equations, Theory Probab. Appl., 45 (2000), pp. 466–479. tba TPRBAU 0040-585X Theor. Probab. Appl. LinkGoogle Scholar[11] E. Pardoux and and A. Yu. Veretennikov, On the Poisson equation and diffusion approximation. I, Ann. Probab., 29 (2001), pp. 1061–1085. anb APBYAE 0091-1798 Ann. Probab. CrossrefGoogle Scholar[12] A. Yu. Veretennikov, Bounds for the mixing rate in the theory of stochastic equations, Theory Probab. Appl., 32 (1987), pp. 273–281. tba TPRBAU 0040-585X Theor. Probab. Appl. LinkGoogle Scholar[13] A. Yu. Veretennikov, The mixing rate and the averaging principle for hypoelliptic stochastic differential equations, Math. USSR‐Izv., 33 (1989), pp. 221–231. axp MUSIAE 0025-5726 Math. USSR, Izv. CrossrefGoogle Scholar[14] A. Yu. Veretennikov and and O. V. Gulinskii, The mixing rate and the averaging principle for recursive stochastic procedures, Automat. Remote Control, 51 (1990), pp. 779–788. aur AURCAT 0005-1179 Autom. Remote Control (Engl. Transl.) Google Scholar[15] A. Yu. Veretennikov, Estimates for the mixing rate for Markov processes, Lithuanian Math. J., 31 (1991), pp. 27–34. aw8 LMJTD6 0363-1672 Lith. Math. J. CrossrefGoogle Scholar[16] A. Yu. Veretennikov, On polynomial mixing bounds for stochastic differential equations, Stochastic Process. Appl., 70 (1997), pp. 115–127. a2m STOPB7 0304-4149 Stochastic Proc. Appl. CrossrefGoogle Scholar[17] A. Yu. Veretennikov, On polynomial mixing and convergence rate for stochastic difference and differential equations, Theory Probab. Appl., 44 (1999), pp. 361–374. tba TPRBAU 0040-585X Theor. Probab. Appl. LinkGoogle ScholarKeywordsMarkov processmixingconvergence to the equilibrium Previous article Next article FiguresRelatedReferencesCited ByDetails Subgeometric ergodicity and β -mixingJournal of Applied Probability, Vol. 58, No. 3 | 16 September 2021 Cross Ref SUBGEOMETRICALLY ERGODIC AUTOREGRESSIONSEconometric Theory, Vol. 17 | 9 November 2020 Cross Ref Stability, Stationarity, ErgodicityAn Introduction to Continuous-Time Stochastic Processes | 1 Jan 2015 Cross Ref Applications to Biology and MedicineAn Introduction to Continuous-Time Stochastic Processes | 1 Jan 2015 Cross Ref Infinite horizon stopping problems with (nearly) total reward criteriaStochastic Processes and their Applications, Vol. 124, No. 12 | 1 Dec 2014 Cross Ref On Local Mixing Conditions for SDE ApproximationsS. A. Klokov and A. Yu. 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