Large Deviations for Stochastic Geometric Wave Equation

Zdzisław Brzeźniak, Beniamin Goldys and Nimit Rana


In this paper we are concerned with stochastic perturbations of the wave map taking values in a compact Riemannian manifold (stochastic wave map). Our main result is the large deviations principle (LDP) for the small noise asymptotics of the solution. Our proof relies on a new version of the weak convergence approach by Budhiraja and Dupuis (Probab. Math. Statist., 2000) suitable for the analysis of stochastic wave maps in local Sobolev spaces.

Keywords: stochastic wave map, Riemannian manifold, infinite dimensional Brownian motion, large deviations principle.

AMS Subject Classification: Primary 60H15; secondary 58D20, 58D25, 53C44.

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Thursday, October 17, 2019