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Bibliographic Details
Main Authors: Okabe, Yasunori, Mano, Hajime, Itoh, Yoshiaki
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2507.00362
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Table of 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.