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Ergodic Property of Stable-Like Markov Chains

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  • Nikola Sandrić

    (University of Zagreb)

Abstract

A stable-like Markov chain is a time-homogeneous Markov chain on the real line with the transition kernel $$p(x,\hbox {d}y)=f_x(y-x)\hbox {d}y$$ p ( x , d y ) = f x ( y - x ) d y , where the density functions $$f_x(y)$$ f x ( y ) , for large $$|y|$$ | y | , have a power-law decay with exponent $$\alpha (x)+1$$ α ( x ) + 1 , where $$\alpha (x)\in (0,2)$$ α ( x ) ∈ ( 0 , 2 ) . In this paper, under a certain uniformity condition on the density functions $$f_x(y)$$ f x ( y ) and additional mild drift conditions, we give sufficient conditions for recurrence in the case when $$0

Suggested Citation

  • Nikola Sandrić, 2016. "Ergodic Property of Stable-Like Markov Chains," Journal of Theoretical Probability, Springer, vol. 29(2), pages 459-490, June.
  • Handle: RePEc:spr:jotpro:v:29:y:2016:i:2:d:10.1007_s10959-014-0586-4
    DOI: 10.1007/s10959-014-0586-4
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    References listed on IDEAS

    as
    1. Nikola Sandrić, 2014. "Recurrence and Transience Criteria for Two Cases of Stable-Like Markov Chains," Journal of Theoretical Probability, Springer, vol. 27(3), pages 754-788, September.
    2. Sandrić, Nikola, 2013. "Long-time behavior of stable-like processes," Stochastic Processes and their Applications, Elsevier, vol. 123(4), pages 1276-1300.
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    Cited by:

    1. Yong-Hua Mao & Yan-Hong Song, 2022. "Criteria for Geometric and Algebraic Transience for Discrete-Time Markov Chains," Journal of Theoretical Probability, Springer, vol. 35(3), pages 1974-2008, September.

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