Long-time behavior of stable-like processes

Nikola Sandrić

Stochastic Processes and their Applications, 2013, vol. 123, issue 4, 1276-1300

Abstract: In this paper, we consider a long-time behavior of stable-like processes. A stable-like process is a Feller process given by the symbol p(x,ξ)=−iβ(x)ξ+γ(x)|ξ|α(x), where α(x)∈(0,2), β(x)∈R and γ(x)∈(0,∞). More precisely, we give sufficient conditions for recurrence, transience and ergodicity of stable-like processes in terms of the stability function α(x), the drift function β(x) and the scaling function γ(x). Further, as a special case of these results we give a new proof for the recurrence and transience property of one-dimensional symmetric stable Lévy processes with the index of stability α≠1.

Keywords: Ergodicity; Foster–Lyapunov criteria; Harris recurrence; Recurrence; Stable-like process; Transience (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (7)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:123:y:2013:i:4:p:1276-1300

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DOI: 10.1016/j.spa.2012.12.004

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