Large deviation principle for stochastic FitzHugh-Nagumo lattice systems (Q6591745)

In the paper, the authors investigate the large deviation principle (LDP) for stochastic FitzHugh-Nagumo lattice systems with locally Lipschitz drift and diffusion terms. The proof relies on weak convergence method. The authors first prove the well-posedness of the deterministic controlled FitzHugh-Nagumo lattice system, then obtain the strong continuity of the solution of such control system (with respect to control in the weak topology). Then they study the convergence in distribution of the solutions of the stochastic control system and, finally, get the LDP using the equivalence of LDP and the Laplace principle. See close results also in [\textit{W. Liu} et al., Sci. China, Math. 63, No. 6, 1181--1202 (2020; Zbl 1451.60070); \textit{B. Wang}, Discrete Contin. Dyn. Syst., Ser. B 29, No. 3, 1319--1343 (2024; Zbl 1543.37076)].