Large Deviations for $(1+1)$-dimensional Stochastic Geometric Wave Equation

Abstract

We consider stochastic wave map equation on real line with solutions taking values in a $d$-dimensional compact Riemannian manifold. We show first that this equation has unique, global, strong in PDE sense, solution in local Sobolev spaces. The main result of the paper is a proof of the Large Deviations Principle for solutions in the case of vanishing noise.

arXiv commentThe current paper is an expanded and corrected version of the previous submission. Major change is the addition of Lemma 5.5. Martin Ondreját's name has been added as a new author. The title of the paper has also been modified to a more suitable one to our results