The lower envelope of positive self-similar Markov processes

2006/01/09 by Loïc Chaumont, Chaumont, Loïc, Juan Carlos Pardo +1 · 1 citation
Economics, Econometrics and Finance · Mathematics · #60 B 10 #60 G 18 #60 G 51 #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.math/0601177

openalex publication_date 2006/01/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish integral tests and laws of the iterated logarithm for the lower envelope of positive self-similar Markov processes at 0 and +∞. Our proofs are based on the Lamperti representation and time reversal arguments. These results extend laws of the iterated logarithm for Bessel processes due to Dvoretsky and Erdös, Motoo and Rivero.

Cited by

• On the passage times of self-similar Gaussian processes on curved boundaries

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