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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2507.00362 |
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| _version_ | 1866913920055246848 |
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| author | Okabe, Yasunori Mano, Hajime Itoh, Yoshiaki |
| author_facet | Okabe, Yasunori Mano, Hajime Itoh, Yoshiaki |
| contents | This paper treats a random collision model of three species, which is represented by the random time change of three standard Poisson processes. The prey-predator relation in the random collision model looks like paper-scissors-stone game, and the model is called the paper-scissors model. At first, we investigate the stochastic structure of our model. By using stochastic calculus, the model is decomposed into a semi-martingale, and we prove a weak law of large numbers and a central limit theorem. The main purpose of this paper is to obtain an ordinary differential equation from the weak law and a stochastic differential equation from the central limit theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_00362 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Paper-Scissors-Stone Model for Interacting Population and its Limit Theorem Okabe, Yasunori Mano, Hajime Itoh, Yoshiaki Probability This paper treats a random collision model of three species, which is represented by the random time change of three standard Poisson processes. The prey-predator relation in the random collision model looks like paper-scissors-stone game, and the model is called the paper-scissors model. At first, we investigate the stochastic structure of our model. By using stochastic calculus, the model is decomposed into a semi-martingale, and we prove a weak law of large numbers and a central limit theorem. The main purpose of this paper is to obtain an ordinary differential equation from the weak law and a stochastic differential equation from the central limit theorem. |
| title | Paper-Scissors-Stone Model for Interacting Population and its Limit Theorem |
| topic | Probability |
| url | https://arxiv.org/abs/2507.00362 |