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On polynomial mixing bounds for stochastic differential equations

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  • Veretennikov, A. Yu.

Abstract

Polynomial bounds for the coefficient of [beta]-mixing are established for diffusion processes under weak recurrency assumptions. The method is based on direct evaluations of the moments and certain functionals of hitting-times of the process and on the change of time.

Suggested Citation

  • Veretennikov, A. Yu., 1997. "On polynomial mixing bounds for stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 70(1), pages 115-127, October.
  • Handle: RePEc:eee:spapps:v:70:y:1997:i:1:p:115-127
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    Cited by:

    1. Chen, Xiaohong & Hansen, Lars Peter & Carrasco, Marine, 2010. "Nonlinearity and temporal dependence," Journal of Econometrics, Elsevier, vol. 155(2), pages 155-169, April.
    2. Shin Kanaya, 2016. "Convergence rates of sums of a-mixing triangular arrays: with an application to non-parametric drift function estimation of continuous-time processes," CREATES Research Papers 2016-24, Department of Economics and Business Economics, Aarhus University.
    3. Masayuki Uchida & Nakahiro Yoshida, 2001. "Information Criteria in Model Selection for Mixing Processes," Statistical Inference for Stochastic Processes, Springer, vol. 4(1), pages 73-98, January.
    4. Shin Kanaya, 2015. "Uniform Convergence Rates of Kernel-Based Nonparametric Estimators for Continuous Time Diffusion Processes: A Damping Function Approach," CREATES Research Papers 2015-50, Department of Economics and Business Economics, Aarhus University.
    5. Song, Yan-Hong, 2016. "Algebraic ergodicity for SDEs driven by Lévy processes," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 108-115.
    6. Yuji Sakamoto & Nakahiro Yoshida, 2009. "Third-order asymptotic expansion of M-estimators for diffusion processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(3), pages 629-661, September.
    7. A. Veretennikov, 1999. "On Castellana–Leadbetter's Condition for Diffusion Density Estimation," Statistical Inference for Stochastic Processes, Springer, vol. 2(1), pages 1-9, January.
    8. Palczewski, Jan & Stettner, Łukasz, 2014. "Infinite horizon stopping problems with (nearly) total reward criteria," Stochastic Processes and their Applications, Elsevier, vol. 124(12), pages 3887-3920.
    9. Kristensen, Dennis, 2004. "Estimation in two classes of semiparametric diffusion models," LSE Research Online Documents on Economics 24739, London School of Economics and Political Science, LSE Library.
    10. Guillin, A. & Liptser, R., 2005. "MDP for integral functionals of fast and slow processes with averaging," Stochastic Processes and their Applications, Elsevier, vol. 115(7), pages 1187-1207, July.
    11. Cayé, Thomas & Herdegen, Martin & Muhle-Karbe, Johannes, 2020. "Scaling limits of processes with fast nonlinear mean reversion," Stochastic Processes and their Applications, Elsevier, vol. 130(4), pages 1994-2031.
    12. Anatolii A. Puhalskii & Michael Jay Stutzer, 2016. "On minimising a portfolio's shortfall probability," Papers 1602.02192, arXiv.org, revised May 2017.
    13. Comte, F. & Merlevède, F., 2005. "Super optimal rates for nonparametric density estimation via projection estimators," Stochastic Processes and their Applications, Elsevier, vol. 115(5), pages 797-826, May.
    14. Nakahiro Yoshida, 2011. "Polynomial type large deviation inequalities and quasi-likelihood analysis for stochastic differential equations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(3), pages 431-479, June.
    15. Gailus, Siragan & Spiliopoulos, Konstantinos, 2017. "Statistical inference for perturbed multiscale dynamical systems," Stochastic Processes and their Applications, Elsevier, vol. 127(2), pages 419-448.
    16. Lukas Gonon & Johannes Muhle-Karbe & Xiaofei Shi, 2019. "Asset Pricing with General Transaction Costs: Theory and Numerics," Papers 1905.05027, arXiv.org, revised Apr 2020.
    17. Bal'azs Gerencs'er & Mikl'os R'asonyi, 2020. "Invariant measures for fractional stochastic volatility models," Papers 2002.04832, arXiv.org.
    18. Charlotte Dion & Sarah Lemler, 2020. "Nonparametric drift estimation for diffusions with jumps driven by a Hawkes process," Statistical Inference for Stochastic Processes, Springer, vol. 23(3), pages 489-515, October.
    19. Campillo, Fabien & Kleptsyna, Marina & Piatnitski, Andrey, 2001. "Homogenization of random parabolic operator with large potential," Stochastic Processes and their Applications, Elsevier, vol. 93(1), pages 57-85, May.
    20. Shoichi Eguchi & Hiroki Masuda, 2019. "Data driven time scale in Gaussian quasi-likelihood inference," Statistical Inference for Stochastic Processes, Springer, vol. 22(3), pages 383-430, October.

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