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Continuous-State Branching Processes and Self-Similarity

Part of: Stochastic processes

Published online by Cambridge University Press:  14 July 2016

A. E. Kyprianou  and
J. C. Pardo
A. E. Kyprianou*
Affiliation:
University of Bath
J. C. Pardo*
Affiliation:
University of Bath
*
∗Postal address: Department of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 7AY, UK.
∗Postal address: Department of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 7AY, UK.
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Abstract

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In this paper we study the α-stable continuous-state branching processes (for α ∈ (1, 2]) and the α-stable continuous-state branching processes conditioned never to become extinct in the light of positive self-similarity. Understanding the interaction of the Lamperti transformation for continuous-state branching processes and the Lamperti transformation for positive, self-similar Markov processes gives access to a number of explicit results concerning the paths of α-stable continuous-state branching processes and α-stable continuous-state branching processes conditioned never to become extinct.

Keywords

Positive, self-similar Markov processLamperti representationstable Lévy processconditioning to stay positivecontinuous-state branching process

MSC classification

Secondary: 60G18: Self-similar processes 60G51: Processes with independent increments; L'evy processes
Type
Research Article
Information
Journal of Applied Probability , Volume 45 , Issue 4 , December 2008 , pp. 1140 - 1160
Copyright
Copyright © Applied Probability Trust 2008 

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