Existence For Mild Solution Of Stochastic Parabolic Anderson Model In Random Potential

Stochastic Partial Differential Equation(SPDE)is a very important analytical tool in many academic researches.In recent years,Stochastic Partial Differential Equation has been applied and developed widely in many fields,which include fluid mechanics,chemistry,financial mathematics and stochastic control.In the 1950s,Anderson[1]who won the Nobel Prize in physics frist presented a typical Stochastic Partial Differential Equation,which also named as Stochastic Parabolic Anderson model.This model has the deep physics background.This paper mainly studies the existence of the Feyman-Kac form of mild solution of Stochastic Parabolic Anderson model in a random potential which is made of Gauss and Poisson potential.This paper mainly consists of the following sections:Chapter One:In the introduction,first we introduce the introduction background of Stochastic Partial Differential Equation and Stochastic Parabolic Anderson model.Then we describe the basic knowledge which would be used in this paper.Finally we introduce the source of Feynman-Kac formula.Chapter Two:The second chapter will first discusse how to solve the mild solution of Stochastic Partial Differential Equation.Then we introuduce the to form and mild solution of Stochastic Parabolic Anderson model.Chapter Three:The third chapter is the main result in this paper.First,in the intro-duction section,giving a type of Stochastic Parabolic Anderson model and the stochastic potential V(t,x).Then studying the definition and properties of stochastic integral.Finally proofing the existence of the Feynman-Kac form of mild solution of Stochastic Parabolic Anderson model.