Large Deviations for Stochastic Geometric Wave Equation

Zdzisław Brzeźniak, Beniamin Goldys and Nimit Rana

Abstract

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.