A Jump Type SDE Approach to Positive Self-Similar Markov Processes

Abstract

We present a new approach to positive self-similar Markov processes (pssMps) by reformulating Lamperti's transformation via jump type SDEs. As applications, we give direct constructions of pssMps (re)started continuously at zero if the Lamperti transformed Levy process is spectrally negative. Our paper can be seen as a continuation of similar studies for continuous state branching processes but the approach seems to be more fruitful in the context of pssMps.

38 pages

References in corpus (3)

• Recurrent extensions of self-similar Markov processes and Cramér's condition II
• Weak convergence of positive self-similar Markov processes and overshoots of Lévy processes
• Hitting properties and non-uniqueness for SDE driven by stable processes

Cited by in corpus (6)

• Hitting properties and non-uniqueness for SDE driven by stable processes
• Multifractality of jump diffusion processes
• Multilevel Monte Carlo simulation for Levy processes based on the Wiener-Hopf factorisation
• Strong solutions of jump-type stochastic equations
• Yamada-Watanabe results for stochastic differential equations with jumps
• On entire moments of self-similar Markov processes