The multiple birth properties of multi-type Markov branching processes
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
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| _version_ | 1866916315535507456 |
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| author | Li, Junping Zhang, Wanting |
| author_facet | Li, Junping Zhang, Wanting |
| contents | The main purpose of this paper is to consider the multiple birth properties for multi-type Markov branching processes. We first construct a new multi-dimensional Markov process based on the multi-type Markov branching process, which can reveal the multiple birth characteristics. Then the joint probability distribution of multiple birth of multi-type Markov branching process until any time $t$ is obtained by using the new process. Furthermore, the probability distribution of multiple birth until the extinction of the process is also given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_05252 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The multiple birth properties of multi-type Markov branching processes Li, Junping Zhang, Wanting Probability The main purpose of this paper is to consider the multiple birth properties for multi-type Markov branching processes. We first construct a new multi-dimensional Markov process based on the multi-type Markov branching process, which can reveal the multiple birth characteristics. Then the joint probability distribution of multiple birth of multi-type Markov branching process until any time $t$ is obtained by using the new process. Furthermore, the probability distribution of multiple birth until the extinction of the process is also given. |
| title | The multiple birth properties of multi-type Markov branching processes |
| topic | Probability |
| url | https://arxiv.org/abs/2407.05252 |