Ergodic Property of Stable-Like Markov Chains

Nikola Sandrić ()
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Nikola Sandrić: University of Zagreb

Journal of Theoretical Probability, 2016, vol. 29, issue 2, 459-490

Abstract: 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

Keywords: Ergodicity; Foster–Lyapunov drift criteria; Recurrence; Stable distribution; Stable-like Markov chain; Transience; 60J05; 60G52 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10959-014-0586-4

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