MOMENTS OF PASSAGE TIMES AND ASYMPTOTIC BEHAVIOR OF INCREASING SELF-SIMILAR MARKOV PROCESSES

doi:10.1016/S0252-9602(15)30064-3

Abstract

Abstract:

By using Lamperti's bijection between self-similar Markov processes and Lévy processes, we prove finiteness of moments and asymptotic behavior of passage times for increasing self-similar Markov processes valued in (0,∞). We also investigate the behavior of the process when it crosses a level. A limit theorem concerning the distribution of the process immediately before it crosses some level is proved. Some useful examples are given.

Key words: self-similar process, Markov process, Lé, vy process, subordinator, passage time, moment

CLC Number:

60G18

Wei HU, Luqin LIU. MOMENTS OF PASSAGE TIMES AND ASYMPTOTIC BEHAVIOR OF INCREASING SELF-SIMILAR MARKOV PROCESSES[J].Acta mathematica scientia,Series B, 2015, 35(6): 1426-1436.

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