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

2011/11/14 by Leif Doering, Doering, Leif, Mátyás Barczy +1 · 2 citations
Mathematics · #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1111.3235

openalex publication_date 2011/11/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Hitting properties and non-uniqueness for SDE driven by stable processes
• On the passage times of self-similar Gaussian processes on curved boundaries

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