Uniqueness Problem for the Backward Differential Equation of a Continuous-State Branching Process
Probability
2024-05-10 v1
Abstract
The distributional properties of a multi-dimensional continuous-state branching process are determined by its cumulant semigroup, which is defined by the backward differential equation. We provide a proof of the assertion of Rhyzhov and Skorokhod (Theory Probab. Appl., 1970) on the uniqueness of the solutions to the equation, which is based on a characterization of the process as the pathwise unique solution to a system of stochastic equations.
Cite
@article{arxiv.2405.05879,
title = {Uniqueness Problem for the Backward Differential Equation of a Continuous-State Branching Process},
author = {Pei-Sen Li and Zenghu Li},
journal= {arXiv preprint arXiv:2405.05879},
year = {2024}
}