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Teor. Veroyatnost. i Primenen., 2004, Volume 49, Issue 1, Pages 21–35 (Mi tvp234)  

This article is cited in 22 scientific papers (total in 22 papers)

On subexponential mixing rate for Markov processes

A. Yu. Veretennikova, S. A. Klokovb

a A. A. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences
b Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Science

Abstract: This paper establishes subexponential bounds for the $t$-mixing and the rate of convergence to invariant measure for homogeneous Markov processes with continuous and discrete time.

Keywords: Markov process, mixing, convergence to the equilibrium.

DOI: https://doi.org/10.4213/tvp234

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English version:
Theory of Probability and its Applications, 2005, 49:1, 110–122

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Received: 05.06.2003

Citation: A. Yu. Veretennikov, S. A. Klokov, “On subexponential mixing rate for Markov processes”, Teor. Veroyatnost. i Primenen., 49:1 (2004), 21–35; Theory Probab. Appl., 49:1 (2005), 110–122

Citation in format AMSBIB
\by A.~Yu.~Veretennikov, S.~A.~Klokov
\paper On subexponential mixing rate for Markov processes
\jour Teor. Veroyatnost. i Primenen.
\yr 2004
\vol 49
\issue 1
\pages 21--35
\jour Theory Probab. Appl.
\yr 2005
\vol 49
\issue 1
\pages 110--122

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    This publication is cited in the following articles:
    1. Veretennikov A.Yu., “On lower bounds for mixing coefficients of Markov diffusions”, From stochastic calculus to mathematical finance: The Shiryaev Festschrift, 2006, 623–633, Springer, Berlin  crossref  mathscinet  zmath  isi
    2. Veretennikov A.Yu., “On ergodic measures for McKean-Vlasov stochastic equations”, Monte Carlo and quasi-Monte Carlo methods 2004, Springer, Berlin, 2006, 471–486  crossref  mathscinet  zmath  isi
    3. Bianchi A., “Nonparametric trend coefficient estimation for multidimensional diffusions”, C. R. Math. Acad. Sci. Paris, 345:2 (2007), 101–105  crossref  mathscinet  zmath  isi  scopus
    4. Capasso V., Morale D., Ortisi M., “Long time behavior of a system of stochastic differential equations modelling aggregation”, Math everywhere: Deterministic and Stochastic Modelling in Biomedicine, Economics and Industry, Springer, Berlin, 2007, 25–38  mathscinet  zmath  isi
    5. Bianchi A., “Invariant density estimation for multidimensional diffusions”, Math everywhere: Deterministic and Stochastic Modelling in Biomedicine, Economics and Industry, Springer, Berlin, 2007, 39–50  mathscinet  zmath  isi
    6. Capasso V., Morale D., “Rescaling stochastic processes: asymptotics”, Multiscale problems in the life sciences, Lecture Notes in Math., 1940, Springer, Berlin, 2008, 91–146  crossref  mathscinet  zmath  isi  scopus
    7. Jasso-Fuentes H., Hernández-Lerma O., “Characterizations of overtaking optimality for controlled diffusion processes”, Appl. Math. Optim., 57:3 (2008), 349–369  crossref  mathscinet  zmath  isi  elib  scopus
    8. V. I. Bogachev, N. V. Krylov, M. Röckner, “Elliptic and parabolic equations for measures”, Russian Math. Surveys, 64:6 (2009), 973–1078  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    9. Hairer M., “How Hot Can a Heat Bath Get?”, Comm. Math. Phys., 292:1 (2009), 131–177  crossref  mathscinet  zmath  adsnasa  isi  scopus
    10. Jasso-Fuentes H., Hernández-Lerma O., “Blackwell optimality for controlled diffusion processes”, J. Appl. Probab., 46:2 (2009), 372–391  crossref  mathscinet  zmath  isi  scopus
    11. Capasso V., Morale D., “Asymptotic Behavior of a System of Stochastic Particles Subject to Nonlocal Interactions”, Stoch. Anal. Appl., 27:3 (2009), 574–603  crossref  mathscinet  zmath  isi  elib  scopus
    12. Jasso-Fuentes H., Hernández-Lerma O., “Ergodic control, bias, and sensitive discount optimality for Markov diffusion processes”, Stoch. Anal. Appl., 27:2 (2009), 363–385  crossref  mathscinet  zmath  isi  scopus
    13. Leonenko N.N., Šuvak N., “Statistical inference for reciprocal gamma diffusion process”, J. Statist. Plann. Inference, 140:1 (2010), 30–51  crossref  mathscinet  zmath  isi  elib  scopus
    14. Kleptsyna M.L., Veretennikov A.Yu., “On discrete time ergodic filters with wrong initial data, 2”, Stochastics, 82:1 (2010), 25–40  crossref  mathscinet  zmath  isi  elib  scopus
    15. N. Abourashchi, A. Yu. Veretennikov, “On stochastic averaging and mixing”, Theory Stoch. Process., 16(32):1 (2010), 111–129  mathnet  mathscinet  zmath
    16. Löcherbach E., Loulcianova D., Loukianov O., “Polynomial bounds in the Ergodic theorem for one-dimensional diffusions and integrability of hitting times”, Ann. Inst. Henri Poincaré Probab. Stat., 47:2 (2011), 425–449  crossref  mathscinet  zmath  adsnasa  isi  scopus
    17. B. V. Bondarev, S. M. Kozyr, “On the convergence rate of the solution of differential equation perturbed by “physical” white noise and the solution of corresponding diffusion equation. Exponential mixing”, Theory Probab. Appl., 56:4 (2011), 562–578  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    18. A. Yu. Veretennikov, S. A. Klokov, “On local mixing conditions for SDE approximations”, Theory Probab. Appl., 57:1 (2013), 110–131  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    19. Loecherbach E. Loukianova D., “Polynomial Deviation Bounds for Recurrent Harris Processes Having General State Space”, ESAIM-Prob. Stat., 17 (2013), 195–218  crossref  mathscinet  zmath  isi  scopus
    20. Palczewski J., Stettner L., “Infinite Horizon Stopping Problems With (Nearly) Total Reward Criteria”, Stoch. Process. Their Appl., 124:12 (2014), 3887–3920  crossref  mathscinet  zmath  isi  scopus
    21. Bally V., Caramellino L., “Convergence and regularity of probability laws by using an interpolation method”, Ann. Probab., 45:2 (2017), 1110–1159  crossref  mathscinet  zmath  isi  scopus
    22. Butkovsky O., Scheutzow M., “Invariant Measures For Stochastic Functional Differential Equations”, Electron. J. Probab., 22 (2017), 98  crossref  mathscinet  zmath  isi  scopus
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