Stochastic Burgers' Equation on the Real Line: Regularity and Moment Estimates

In this project we investigate the stochastic Burgers' equation with multiplicative space-time white noise on an unbounded spatial domain. We give a random field solution to this equation by defining a process via a kind of Feynman-Kac representation which solves a stochastic partial differential equation such that its Hopf-Cole transformation solves Burgers' equation. Finally, we obtain H\"older regularity and moment estimates for the solution to Burgers' equation.