Given a real function , the rate function for the large deviations of the diffusion process of drift given by the Freidlin–Wentzell theorem coincides with the time integral of the energy dissipation for the gradient flow associated with . This paper is concerned with the stability in the hilbertian framework of this common action functional when varies. More precisely, we show that if is uniformly -convex for some and converges towards in the sense of Mosco convergence, then the related functionals -converge in the strong topology of curves.
Cite this article
Luigi Ambrosio, Aymeric Baradat, Yann Brenier, -convergence for a class of action functionals induced by gradients of convex functions. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 32 (2021), no. 1, pp. 97–108DOI 10.4171/RLM/928