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Jump type SDEs for self-similar processes. (English) Zbl 1286.60036

Summary: 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 Lévy process is spectrally negative. Our paper can be seen as a continuation of similar studies for continuous state branching processes.

MSC:

60G18 Self-similar stochastic processes
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60G51 Processes with independent increments; Lévy processes
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