Comparison between the Deterministic and Stochastic Models of Nonlocal Diffusion

Itsuki Watanabe1, Hiroshi Toyoizumi2
1Department of Pure and Applied Mathematics, School of Fundamental Science and Engineering, Waseda University, Tokyo, Japan
2Graduate School of Fundamental Science and Engineering, Waseda University, Tokyo, Japan

Tóm tắt

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.

Tài liệu tham khảo

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