Recurrent extensions of self-similar Markov processes and Cramér's condition. II

DOI10.3150/07-BEJ6082zbMath1132.60056arXiv0711.4442OpenAlexW2155247738MaRDI QIDQ2469665

Víctor Manuel Rivero

Publication date: 6 February 2008

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0711.4442

zbMATH Keywords

Lévy processesexcursion theoryLamperti's transformationself-similar Markov processesexponential functionals of Lévy processes

Mathematics Subject Classification ID

Continuous-time Markov processes on general state spaces (60J25) Self-similar stochastic processes (60G18)

Related Items (17)

A jump-type SDE approach to real-valued self-similar Markov processes ⋮ Tail asymptotics for exponential functionals of Lévy processes: the convolution equivalent case ⋮ Positive self-similar Markov processes obtained by resurrection ⋮ Fluctuations of stable processes and exponential functionals of hypergeometric Lévy processes ⋮ Recurrent extensions of real-valued self-similar Markov processes ⋮ Functional limit theorems for processes pieced together from excursions ⋮ Entrance laws at the origin of self-similar Markov processes in high dimensions ⋮ Fluctuation theory and exit systems for positive self-similar Markov processes ⋮ On the distribution of exponential functionals for Lévy processes with jumps of rational transform ⋮ Bouncing skew Brownian motions ⋮ On Entire Moments of Self-Similar Markov Processes ⋮ Hitting properties and non-uniqueness for SDEs driven by stable processes ⋮ Quasi-stationary distributions and Yaglom limits of self-similar Markov processes ⋮ Exponential functionals of spectrally one-sided Lévy processes conditioned to stay positive ⋮ Stable Lévy processes in a cone ⋮ The extended hypergeometric class of Lévy processes ⋮ General self-similarity properties for Markov processes and exponential functionals of Lévy processes

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• Recurrent extensions of self-similar Markov processes and Cramér's condition
• On construction of Markov processes
• Semi-stable Markov processes. I
• Strong Renewal Theorems with Infinite Mean

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