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.
| Original language | English |
|---|---|
| Pages (from-to) | 1825-1836 |
| Number of pages | 12 |
| Journal | Acta Mathematica Sinica, English Series |
| Volume | 40 |
| Issue number | 8 |
| DOIs | |
| Publication status | Published - Aug 2024 |
Keywords
- 60H20
- 60J80
- Continuous-state branching process
- backward differential equation
- generator
- multi-dimensional
- stochastic equation