Given a real function f , the rate function for the large deviations of the di usion process of drift 'f given by the Freidlin-Wentzell theorem coincides with the time integral of the energy dissipation for the gradient flow associated with f . This paper is concerned with the stability in the hilbertian framework of this common action functional when f varies. More precisely, we show that if (fh)h is uniformly λ-convex for some λ ∈ R and converges towards f in the sense of Mosco convergence, then the related functionals G-converge in the strong topology of curves.
Γ-convergence for a class of action functionals induced by gradients of convex functions
Ambrosio L.
;Brenier Y.
2021
Abstract
Given a real function f , the rate function for the large deviations of the di usion process of drift 'f given by the Freidlin-Wentzell theorem coincides with the time integral of the energy dissipation for the gradient flow associated with f . This paper is concerned with the stability in the hilbertian framework of this common action functional when f varies. More precisely, we show that if (fh)h is uniformly λ-convex for some λ ∈ R and converges towards f in the sense of Mosco convergence, then the related functionals G-converge in the strong topology of curves.File in questo prodotto:
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RLM-2021-032-001-05.pdf
Open Access dal 22/04/2022
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