Paper-Scissors-Stone Model for Interacting Population and its Limit Theorem
Probability
2025-07-02 v1
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.
Cite
@article{arxiv.2507.00362,
title = {Paper-Scissors-Stone Model for Interacting Population and its Limit Theorem},
author = {Yasunori Okabe and Hajime Mano and Yoshiaki Itoh},
journal= {arXiv preprint arXiv:2507.00362},
year = {2025}
}