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Asymptotic behaviour near extinction of continuous-state branching processes

Part of: Stochastic processes

Published online by Cambridge University Press:  21 June 2016

Gabriel Berzunza  and
Juan Carlos Pardo
Gabriel Berzunza*
Affiliation:
Universität Zürich
Juan Carlos Pardo*
Affiliation:
Centro de Investigación en Matemáticas
*
* Postal address: Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland. Email address: gabriel.berzunza@math.uzh.ch
** Postal address: Centro de Investigación en Matemáticas, A.C. Calle Jalisco s/n, 36240 Guanajuato, México. Email address: jcpardo@cimat.mx
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Abstract

In this paper we study the asymptotic behaviour near extinction of (sub-)critical continuous-state branching processes. In particular, we establish an analogue of Khintchine's law of the iterated logarithm near extinction time for a continuous-state branching process whose branching mechanism satisfies a given condition.

Keywords

Continuous-state branching processLamperti transformLévy processconditioning to stay positiverate of growth

MSC classification

Primary: 60G17: Sample path properties
Secondary: 60G51: Processes with independent increments; L'evy processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 53 , Issue 2 , June 2016 , pp. 381 - 391
Copyright
Copyright © Applied Probability Trust 2016 

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