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

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 \(d ζ_t = [\Delta_p ζ_t - β ⋅ ζ_t^k] d t + \sqrt{α ⋅ ζ_t^ℓ} d B_t\) with arbitrary initial condition \(ζ_0 \in R^V\). Here, \(\Delta_p\) is the diffusion on V corresponding to p, α, β are positive real numbers and k, ℓ are positive integers.

Recommended citation: C. da Costa, B. F. P. da Costa, M. Jara. "Reaction–Diffusion models: From particle systems to SDE's". Stochastic Processes and their Applications 129 (2019), no. 11, p. 4411-4430.
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