IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v119y2016icp108-115.html
   My bibliography  Save this article

Algebraic ergodicity for SDEs driven by Lévy processes

Author

Listed:
  • Song, Yan-Hong

Abstract

In the paper, a sufficient condition for the algebraic ergodicity for stochastic differential equations driven by Lévy processes is presented. The method is based on direct evaluations of the algebraic moment for the hitting time to some set.

Suggested Citation

  • Song, Yan-Hong, 2016. "Algebraic ergodicity for SDEs driven by Lévy processes," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 108-115.
    • Handle: RePEc:eee:stapro:v:119:y:2016:i:c:p:108-115
    DOI: 10.1016/j.spl.2016.07.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715216301201
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2016.07.004?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Deng, Chang-Song & Schilling, René L., 2015. "On shift Harnack inequalities for subordinate semigroups and moment estimates for Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 125(10), pages 3851-3878.
    2. Mao, Yong-Hua & Song, Yan-Hong, 2014. "On geometric and algebraic transience for discrete-time Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 124(4), pages 1648-1678.
    3. Sandrić, Nikola, 2013. "Long-time behavior of stable-like processes," Stochastic Processes and their Applications, Elsevier, vol. 123(4), pages 1276-1300.
    4. 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.
    5. Wang, Jian, 2008. "Criteria for ergodicity of Lévy type operators in dimension one," Stochastic Processes and their Applications, Elsevier, vol. 118(10), pages 1909-1928, October.
    6. Masuda, Hiroki, 2007. "Ergodicity and exponential [beta]-mixing bounds for multidimensional diffusions with jumps," Stochastic Processes and their Applications, Elsevier, vol. 117(1), pages 35-56, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. Fageot, Julien & Fallah, Alireza & Unser, Michael, 2017. "Multidimensional Lévy white noise in weighted Besov spaces," Stochastic Processes and their Applications, Elsevier, vol. 127(5), pages 1599-1621.
    4. Guo, Junyu & Guo, Xiaotian & Xie, Longjie, 2021. "Quantitative stability estimates for multiscale stochastic dynamical systems," Statistics & Probability Letters, Elsevier, vol. 178(C).
    5. Chang-Song Deng, 2020. "Subgeometric Rates of Convergence for Discrete-Time Markov Chains Under Discrete-Time Subordination," Journal of Theoretical Probability, Springer, vol. 33(1), pages 522-532, March.
    6. Kanaya, Shin, 2017. "Uniform Convergence Rates Of Kernel-Based Nonparametric Estimators For Continuous Time Diffusion Processes: A Damping Function Approach," Econometric Theory, Cambridge University Press, vol. 33(4), pages 874-914, August.
    7. Anatolii A. Puhalskii, 2003. "On Large Deviation Convergence of Invariant Measures," Journal of Theoretical Probability, Springer, vol. 16(3), pages 689-724, July.
    8. 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.
    9. Chen, Xiaohong & Hansen, Lars Peter & Carrasco, Marine, 2010. "Nonlinearity and temporal dependence," Journal of Econometrics, Elsevier, vol. 155(2), pages 155-169, April.
    10. Mattingly, J. C. & Stuart, A. M. & Higham, D. J., 2002. "Ergodicity for SDEs and approximations: locally Lipschitz vector fields and degenerate noise," Stochastic Processes and their Applications, Elsevier, vol. 101(2), pages 185-232, October.
    11. Schmisser, Émeline, 2019. "Non parametric estimation of the diffusion coefficients of a diffusion with jumps," Stochastic Processes and their Applications, Elsevier, vol. 129(12), pages 5364-5405.
    12. 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.
    13. 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.
    14. 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.
    15. Anatolii A. Puhalskii & Michael Jay Stutzer, 2016. "On minimising a portfolio's shortfall probability," Papers 1602.02192, arXiv.org, revised May 2017.
    16. Hiroki Masuda & Lorenzo Mercuri & Yuma Uehara, 2024. "Quasi-likelihood analysis for Student-Lévy regression," Statistical Inference for Stochastic Processes, Springer, vol. 27(3), pages 761-794, October.
    17. Alexander Veretennikov, 2023. "Polynomial Recurrence for SDEs with a Gradient-Type Drift, Revisited," Mathematics, MDPI, vol. 11(14), pages 1-16, July.
    18. E. Löcherbach, 2020. "Convergence to Equilibrium for Time-Inhomogeneous Jump Diffusions with State-Dependent Jump Intensity," Journal of Theoretical Probability, Springer, vol. 33(4), pages 2280-2314, December.
    19. Sangyeol Lee & Hiroki Masuda, 2010. "Jarque–Bera normality test for the driving Lévy process of a discretely observed univariate SDE," Statistical Inference for Stochastic Processes, Springer, vol. 13(2), pages 147-161, June.
    20. Xinghu Jin & Tian Shen & Zhonggen Su, 2023. "Using Stein’s Method to Analyze Euler–Maruyama Approximations of Regime-Switching Jump Diffusion Processes," Journal of Theoretical Probability, Springer, vol. 36(3), pages 1797-1828, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:119:y:2016:i:c:p:108-115. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.