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

Zdzisław Brzeźniak; Ben Goldys; Martin Ondreját; Nimit Rana

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arXiv · 2006.07108

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

Zdzisław Brzeźniak·Ben Goldys·Martin Ondreját·Nimit Rana

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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.

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Zdzisław Brzeźniak, Ben Goldys, Martin Ondreját, Nimit Rana. 2020-06-12. Large Deviations for $(1+1)$-dimensional Stochastic Geometric Wave Equation. https://arxiv.org/abs/2006.07108

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