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

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

2011-11-14

arxiv.org/abs/1111.3235v1

Mathematics

Probability

38 pages

Scientific paper

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.

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