Electronic Communications in Probability

On SDE associated with continuous-state branching processes conditioned to never be extinct

Maria Fittipaldi and Joaquin Fontbona

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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.

Article information

Source
Electron. Commun. Probab., Volume 17 (2012), paper no. 49, 13 pp.

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465263182

Digital Object Identifier
doi:10.1214/ECP.v17-1972

Mathematical Reviews number (MathSciNet)
MR2988395

Zentralblatt MATH identifier
1252.60087

Subjects
Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60H20: Stochastic integral equations 60H10: Stochastic ordinary differential equations [See also 34F05]

Keywords
Stochastic Differential Equations Continuous-state branching processes Non-extinction Immigration

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

Fittipaldi, Maria; Fontbona, Joaquin. On SDE associated with continuous-state branching processes conditioned to never be extinct. Electron. Commun. Probab. 17 (2012), paper no. 49, 13 pp. doi:10.1214/ECP.v17-1972. https://projecteuclid.org/euclid.ecp/1465263182


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