Paper-Scissors-Stone Model for Interacting Population and its Limit Theorem

Yasunori Okabe; Hajime Mano; Yoshiaki Itoh

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arXiv · 2507.00362

Paper-Scissors-Stone Model for Interacting Population and its Limit Theorem

Yasunori Okabe·Hajime Mano·Yoshiaki Itoh

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Abstract

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.

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BibTeX RIS

Yasunori Okabe, Hajime Mano, Yoshiaki Itoh. 2025-07-01. Paper-Scissors-Stone Model for Interacting Population and its Limit Theorem. https://arxiv.org/abs/2507.00362

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