Uniqueness Problem for the Backward Differential Equation of a Continuous-State Branching Process
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913345359052800 |
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| author | Li, Pei-Sen Li, Zenghu |
| author_facet | Li, Pei-Sen Li, Zenghu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_05879 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Uniqueness Problem for the Backward Differential Equation of a Continuous-State Branching Process Li, Pei-Sen Li, Zenghu Probability 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. |
| title | Uniqueness Problem for the Backward Differential Equation of a Continuous-State Branching Process |
| topic | Probability |
| url | https://arxiv.org/abs/2405.05879 |