Comparison between the Deterministic and Stochastic Models of Nonlocal Diffusion

Itsuki Watanabe*, Hiroshi Toyoizumi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
JournalJournal of Dynamics and Differential Equations
DOIs
Publication statusAccepted/In press - 2022

Keywords

  • Law of large numbers
  • Nonlocal diffusion
  • Reaction-diffusion equation
  • Stochastic evolution equation
  • Weak convergence

ASJC Scopus subject areas

  • Analysis

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