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| Content Provider | Springer Nature Link |
|---|---|
| Author | Sandrić, Nikola |
| Copyright Year | 2014 |
| Abstract | A stable-like Markov chain is a time-homogeneous Markov chain on the real line with the transition kernel $$p(x,\hbox {d}y)=f_x(y-x)\hbox {d}y$$ , where the density functions $$f_x(y)$$ , for large $$|y|$$ , have a power-law decay with exponent $$\alpha (x)+1$$ , where $$\alpha (x)\in (0,2)$$ . In this paper, under a certain uniformity condition on the density functions $$f_x(y)$$ and additional mild drift conditions, we give sufficient conditions for recurrence in the case when $$0<\liminf _{|x|\longrightarrow \infty }\alpha (x)$$ , sufficient conditions for transience in the case when $$\limsup _{|x|\longrightarrow \infty }\alpha (x)<2$$ and sufficient conditions for ergodicity in the case when $$0<\inf \{\alpha (x):x\in \mathbb {R}\}$$ . As a special case of these results, we give a new proof for the recurrence and transience property of a symmetric $$\alpha $$ -stable random walk on $$\mathbb {R}$$ with the index of stability $$\alpha \ne 1$$ . |
| Starting Page | 459 |
| Ending Page | 490 |
| Page Count | 32 |
| File Format | |
| ISSN | 08949840 |
| Journal | Journal of Theoretical Probability |
| Volume Number | 29 |
| Issue Number | 2 |
| e-ISSN | 15729230 |
| Language | English |
| Publisher | Springer US |
| Publisher Date | 2014-12-05 |
| Publisher Place | New York |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | Ergodicity Foster–Lyapunov drift criteria Recurrence Stable distribution Stable-like Markov chain Transience Probability Theory and Stochastic Processes Statistics |
| Content Type | Text |
| Resource Type | Article |
| Subject | Statistics and Probability Statistics, Probability and Uncertainty |
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