The upper envelope of positive self-similar Markov processes
نویسندگان
چکیده
We establish integral tests and 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, time reversal arguments and on the study of the upper envelope of their future infimum due to Pardo [19]. These results extend integral test and laws of the iterated logarithm for Bessel processes due to Dvoretsky and Erdös [10] and stable Lévy processes conditioned to stay positive with no positive jumps due to Bertoin [1]. Lévy process, Lamperti representation, First and last passage time, integral test, law of the iterated logarithm.
منابع مشابه
On the future infimum of positive self-similar Markov processes
On the future infimum of positive self-similar Markov processes. Abstract We establish integral tests and laws of the iterated logarithm for the upper envelope of the future infimum of positive self-similar Markov processes and for increasing self-similar Markov processes at 0 and +∞. Our proofs are based on the Lamperti representation and time reversal arguments due to Chaumont and Pardo [9]. ...
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