The Upper Envelope of Positive Self-Similar Markov Processes

被引：0
|
作者：
J. C. Pardo
机构：
[1] Université Pierre et Marie Curie,Laboratoire de Probabilités et Modèles Aléatoires
来源：
Journal of Theoretical Probability | 2009年 / 22卷
关键词：
Self-similar Markov process; Self-similar additive processes; Future infimum process; Lévy process; Lamperti representation; First and last passage time; Integral test; Law of the iterated logarithm; 60G18; 60G17; 60G51; 60F15;
D O I：
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中图分类号：
学科分类号：
摘要：
We establish integral tests in connection with laws of the iterated logarithm at 0 and at +∞, for the upper envelope of positive self-similar Markov processes. Our arguments are based on the Lamperti representation and on the study of the upper envelope of the future infimum due to the author (see Pardo in Stoch. Stoch. Rep. 78:123–155, [2006]). These results extend laws of the iterated logarithm for Bessel processes due to Dvoretsky and Erdős (Proceedings of the Second Berkeley Symposium, [1951]) and stable Lévy processes with no positive jumps conditioned to stay positive due to Bertoin (Stoch. Process. Appl. 55:91–100, [1995]).
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页码：514 / 542
页数：28
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