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

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.

References in corpus (6)

• Skew convolution semigroups and affine Markov processes
• Stochastic equations, flows and measure-valued processes
• Proof(s) of the Lamperti representation of Continuous-State Branching Processes
• Path-valued branching processes and nonlocal branching superprocesses
• A Williams' Decomposition for Spatially Dependent Superprocesses
• Change of measure in the lookdown particle system

Cited by in corpus (4)

• Stochastic differential equation with jumps for multi-type continuous state and continuous time branching processes with immigration
• Skeletal stochastic differential equations for superprocesses
• Construction of continuous-state branching processes in varying environments
• Skeletal stochastic differential equations for continuous-state branching process