Comparison between the Deterministic and Stochastic Models of Nonlocal Diffusion

Itsuki Watanabe*, Hiroshi Toyoizumi

*この研究の対応する著者

研究成果: Article査読

抄録

In this paper, we discuss the difference between the deterministic and stochastic models of nonlocal diffusion. We use a nonlocal reaction-diffusion equation and a multi-dimensional jump Markov process to analyze these mathematical models. First, we demonstrate that the difference converges to 0 in probability with a supremum norm for a sizeable network. Next, we consider the rescaled difference and show that it converges to a stochastic process in distribution on the Skorokhod space.

本文言語English
ジャーナルJournal of Dynamics and Differential Equations
DOI
出版ステータスAccepted/In press - 2022

ASJC Scopus subject areas

  • 分析

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