Abstract:
The existence and uniqueness of the invariant measure is proved for a stochastic differential equation. The conditions for the drift coefficient are obtained which provide a subexponential rate of convergence to the invariant measure as well as a subexponential rate of convergence of the Kolmogorov mixing coefficients.
Citation:
M. N. Malyshkin, “Subexponential estimates of the rate of convergence to the invariant measure for stochastic differential equations”, Teor. Veroyatnost. i Primenen., 45:3 (2000), 489–504; Theory Probab. Appl., 45:3 (2001), 466–479
\Bibitem{Mal00}
\by M.~N.~Malyshkin
\paper Subexponential estimates of the rate of convergence to the invariant measure for stochastic differential equations
\jour Teor. Veroyatnost. i Primenen.
\yr 2000
\vol 45
\issue 3
\pages 489--504
\mathnet{http://mi.mathnet.ru/tvp481}
\crossref{https://doi.org/10.4213/tvp481}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1967786}
\zmath{https://zbmath.org/?q=an:0994.60062}
\transl
\jour Theory Probab. Appl.
\yr 2001
\vol 45
\issue 3
\pages 466--479
\crossref{https://doi.org/10.1137/S0040585X97978403}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000170561800007}
Linking options:
https://www.mathnet.ru/eng/tvp481
https://doi.org/10.4213/tvp481
https://www.mathnet.ru/eng/tvp/v45/i3/p489
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Kulik A. Pavlyukevich I., “Moment Bounds For Dissipative Semimartingales With Heavy Jumps”, Stoch. Process. Their Appl., 141 (2021), 274–308
Sarantsev A., “Sub-Exponential Rate of Convergence to Equilibrium For Processes on the Half-Line”, Stat. Probab. Lett., 175 (2021), 109115
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Song Ya.-H., “Algebraic ergodicity for SDEs driven by Lévy processes”, Stat. Probab. Lett., 119 (2016), 108–115
Puhalskii A.A., “On large deviations of coupled diffusions with time scale separation”, Ann. Probab., 44:4 (2016), 3111–3186
Butkovsky O., “Subgeometric Rates of Convergence of Markov Processes in the Wasserstein Metric”, Ann. Appl. Probab., 24:2 (2014), 526–552
A. I. Noarov, “On some diffusion processes with stationary distributions”, Theory Probab. Appl., 54:3 (2010), 525–533
Douc R., Fort G., Guillin A., “Subgeometric rates of convergence of f–ergodic strong Markov processes”, Stochastic Processes and Their Applications, 119:3 (2009), 897–923
S. A. Klokov, “On law bounds for mixing rates for a class of Markov processes”, Theory Probab. Appl., 51:3 (2007), 528–535
Givon D., Kevrekidis I.G., Kupferman R., “Strong convergence of projective integration schemes for singularly perturbed stochastic differential systems”, Communications in Mathematical Sciences, 4:4 (2006), 707–729
Veretennikov A.Y., “On lower bounds for mixing coefficients of Markov diffusions”, From Stochastic Calculus to Mathematical Finance: The Shiryaev Festschrift, 2006, 623–633
Fort G., Roberts G.O., “Subgeometric ergodicity of strong Markov processes”, Annals of Applied Probability, 15:2 (2005), 1565–1589
A. Yu. Veretennikov, S. A. Klokov, “On subexponential mixing rate for Markov processes”, Theory Probab. Appl., 49:1 (2005), 110–122
Douc R., Fort G., Moulines E., Soulier P., “Practical drift conditions for subgeometric rates of convergence”, Annals of Applied Probability, 14:3 (2004), 1353–1377
Puhalskii A.A., “On large deviation convergence of invariant measures”, Journal of Theoretical Probability, 16:3 (2003), 689–724
A. Yu. Veretennikov, “On polynomial mixing for SDEs with a gradient-type drift”, Theory Probab. Appl., 45:1 (2001), 160–164
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