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Algebraic ergodicity for SDEs driven by Lévy processes

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  • 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
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    References listed on IDEAS

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    1. 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.
    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. 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.
    4. Sandrić, Nikola, 2013. "Long-time behavior of stable-like processes," Stochastic Processes and their Applications, Elsevier, vol. 123(4), pages 1276-1300.
    5. 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.
    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.
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