Year: 2025
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Okabe, Yasunori, Mano, Hajime, Itoh, Yoshiaki
Institution: The Institute of Statistical Mathematics
Language: English
Field: Medicine
Domain: Health Sciences
Open Access status: green
OpenAlex ID: W4416872800
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