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| $\alpha$-TRANSIENCE AND $\alpha$-RECURRENCE FOR RANDOM WALKS AND LEVY PROCESSES |
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Citation： |
ZHANG Huizeng,ZHAO Minzhi,YING Jiangang.$\alpha$-TRANSIENCE AND $\alpha$-RECURRENCE FOR RANDOM WALKS AND LEVY PROCESSES[J].Chinese Annals of Mathematics B,2005,26(1):127~142 |
| Page view： 1180
Net amount： 860 |
Authors： |
ZHANG Huizeng; ZHAO Minzhi;YING Jiangang |
Foundation： |
Project supported by the National Natural Science Foundation of China (No.10271109). |
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| Abstract： |
The authors investigate the
$\alpha$-transience and $\alpha$-recurrence for random walks and Levy processes by means of the associated moment
generating function, give a dichotomy
theorem for not one-sided processes and prove that the process $X$ is quasi-symmetric if and only if $X$
is not $\alpha$-recurrent for all $\alpha<0$ which gives a probabilistic explanation of quasi-symmetry, a concept
originated from C. J. Stone. |
Keywords： |
$\alpha$-Transience, $\alpha$-Recurrence, Quasi-symmetry, Levy
process |
Classification： |
60G51 |
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