Reaction–Diffusion models: From particle systems to SDE’s

Conrado da Costa, Bernardo Freitas Paulo da Costa and Milton Jara

Stochastic Processes and their Applications, 2019, vol. 129, issue 11, 4411-4430

Abstract: Let V be any finite set and p(⋅,⋅) a transition kernel on it. We present a construction of a family of Reaction–Diffusion models that converge after scaling to the solution to the |V|-dimensional SDE: dζt=[Δpζt−β⋅ζtk]dt+α⋅ζtℓdBtwith arbitrary initial condition ζ0∈RV. Here, Δp is the diffusion on V corresponding to p, α, β are positive real numbers and k, ℓ are positive integers.

Keywords: Reaction–Diffusion models; Scaling limit of particle systems; Stochastic differential equations; Martingale problems (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2018.12.004

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