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Law of large numbers in the supremum norm for a chemical reaction with diffusion. (English) Zbl 0747.60033
Refining earlier results of Kotelenez (1982-88), the author proves a theorem on space-time compactly uniform asymptotic consistency in probability of a random, discrete space, jump Markov model for the solution of the usual reaction-diffusion equation. The new theorem works in both linear and nonlinear settings, under conditions shown to be minimal. Also some exponential estimates to the convergence rate are obtained.
60F17Functional limit theorems; invariance principles
60K35Interacting random processes; statistical mechanics type models; percolation theory
60H05Stochastic integrals