Large Deviations for a Class of Parabolic Semilinear Stochastic Partial Differential Equations in Any Space Dimension

#### L. Setayeshgar

2019, v.25, Issue 5, 899-914

ABSTRACT

We prove the large deviation principle for the law of the solutions to a class of parabolic semilinear stochastic partial differential equations driven by multiplicative noise, in $C\big([0,T]:L^\rho(D)\big)$, where $D\subset {\mathbb R}^d$ with $d\geqslant 1$ is a bounded convex domain with smooth boundary and $\rho$ is any real, positive and large enough number. The equation has nonlinearities of polynomial growth of any order, the space variable is of any dimension, and the proof is based on the weak convergence method.

Keywords: large deviations, stochastic partial differential equations, infinite dimensional dynamical systems