Electronic Journal of Probability

Jump type SDEs for self-similar processes

Leif Döring and Matyas Barczy

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

Article information

Source
Electron. J. Probab., Volume 17 (2012), paper no. 94, 39 pp.

Dates
Accepted: 30 October 2012
First available in Project Euclid: 4 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465062416

Digital Object Identifier
doi:10.1214/EJP.v17-2402

Mathematical Reviews number (MathSciNet)
MR2994842

Zentralblatt MATH identifier
1286.60036

Subjects
Primary: 60G18: Self-similar processes 60H15: Stochastic partial differential equations [See also 35R60]
Secondary: 60G51: Processes with independent increments; Lévy processes

Keywords
Lévy process self-similar Markov process Lamperti's transformation jump type SDEs

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Döring, Leif; Barczy, Matyas. Jump type SDEs for self-similar processes. Electron. J. Probab. 17 (2012), paper no. 94, 39 pp. doi:10.1214/EJP.v17-2402. https://projecteuclid.org/euclid.ejp/1465062416


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