TY - JOUR
T1 - Comparison between the Deterministic and Stochastic Models of Nonlocal Diffusion
AU - Watanabe, Itsuki
AU - Toyoizumi, Hiroshi
N1 - Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2022
Y1 - 2022
N2 - 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.
AB - 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.
KW - Law of large numbers
KW - Nonlocal diffusion
KW - Reaction-diffusion equation
KW - Stochastic evolution equation
KW - Weak convergence
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U2 - 10.1007/s10884-022-10135-4
DO - 10.1007/s10884-022-10135-4
M3 - Article
AN - SCOPUS:85125070967
SN - 1040-7294
JO - Journal of Dynamics and Differential Equations
JF - Journal of Dynamics and Differential Equations
ER -