Minicourse: Some aspects of stochastic heat equations; Part 1
Yaozhong Hu (University of Kansas) gives a minicourse with the title: Some aspects of stochastic heat equations.
I will start with the deterministic heat equation with a potential and prove the well-known Feynman-Kac formula. Then I will introduce the stochastic integral with respect to Gaussian fields. Feynman-Kac formulas for the solution and for the moments of the solution will then established. These formulas will be applied to obtain the sharp upper and lower bounds for the moments of the solution.