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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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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

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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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