Large Deviations For Gaussian Perturbations Of Heat Equation

We study the heat equation in the infinite interval of space subject to a Gaussian noise, white in time and color in spaceFirst we introduce the stochastic integral about the Gaussian noise. Then in Chapter 2 we study of large deviations and the action functional for Gaussian noise. In Chapter3 we give a solution of the above stochastic partial differential equation, deduce that the large deviations principle holds for the stochastic process defined by it and calculate its action functional.