The Large Deviation of Semi-linear Stochastic Partial Differential Equation Driven by Brownian Sheet

Abstract

We prove the large deviation principle for the law of the one-dimensional semi-linear stochastic partial differential equations driven by a nonlinear multiplicative noise. Firstly, combining the energy estimate and approximation procedure, we obtain the existence of the global solution. Secondly, the large deviation principle is obtained via the weak convergence method.

Keywords

Large deviation principle / Stochastic Burgers equation / Weak convergence method / Uniform Laplace principle / 60H15 / 35R30

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Funding

National Natural Science Foundation of China(12171084)

RIGHTS & PERMISSIONS

School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag GmbH Germany, part of Springer Nature