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2012 On SDE associated with continuous-state branching processes conditioned to never be extinct
Maria Fittipaldi, Joaquin Fontbona
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Electron. Commun. Probab. 17: 1-13 (2012). DOI: 10.1214/ECP.v17-1972

Abstract

We study the pathwise description of a (sub-)critical continuous-state branching process (CSBP) conditioned to be never extinct, as the solution to a stochastic differential equation driven by Brownian motion and Poisson point measures. The interest of our approach, which relies on applying Girsanov theorem on the SDE that describes the unconditioned CSBP, is that it points out an explicit mechanism to build the immigration term appearing in the conditioned process, by randomly selecting jumps of the original one. These techniques should also be useful to represent more general $h$-transforms of diffusion-jump processes.

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Maria Fittipaldi. Joaquin Fontbona. "On SDE associated with continuous-state branching processes conditioned to never be extinct." Electron. Commun. Probab. 17 1 - 13, 2012. https://doi.org/10.1214/ECP.v17-1972

Information

Accepted: 9 October 2012; Published: 2012
First available in Project Euclid: 7 June 2016

zbMATH: 1252.60087
MathSciNet: MR2988395
Digital Object Identifier: 10.1214/ECP.v17-1972

Subjects:
Primary: 60J80
Secondary: 60H10, 60H20

JOURNAL ARTICLE
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