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

Probability 2021-10-26 v2

Abstract

We consider stochastic wave map equation on real line with solutions taking values in a dd-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.

Keywords

Cite

@article{arxiv.2006.07108,
  title  = {Large Deviations for $(1+1)$-dimensional Stochastic Geometric Wave Equation},
  author = {Zdzisław Brzeźniak and Ben Goldys and Martin Ondreját and Nimit Rana},
  journal= {arXiv preprint arXiv:2006.07108},
  year   = {2021}
}

Comments

The current paper is an expanded and corrected version of the previous submission. Major change is the addition of Lemma 5.5. Martin Ondrej\'at'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

R2 v1 2026-06-23T16:16:21.832Z