Stochastic Partial Differential Equations
This set of notes developed by the author provides a concise introduction to the classical theory of stochastic partial differential equations. The book assumes a basic knowledge of probability and begins with a number of motivating examples. The main types of equations under consideration are of the form ∂𝑢∂𝑡(𝑡,𝑥)=𝐹(𝑡,𝑥,𝑢(𝑡,𝑥),𝐷𝑢(𝑡,𝑥),𝐷2𝑢(𝑡,𝑥))+𝐺(𝑡,𝑥,𝑢(𝑡,𝑥),𝐷𝑢(𝑡,𝑥))𝑊(𝑡,𝑥)∂u∂t(t,x)=F(t,x,u(t,x),Du(t,x),D2u(t,x))+G(t,x,u(t,x),Du(t,x))W(t,x) and the semi-linear case ∂𝑢∂𝑡(𝑡,𝑥)=Δ𝑢+𝑓(𝑡,𝑥,𝑢(𝑡,𝑥))+𝑔(𝑡,𝑥,𝑢(𝑡,𝑥))𝑊(𝑡,𝑥)∂u∂t(t,x)=Δu+f(t,x,u(t,x))+g(t,x,u(t,x))W(t,x) where 𝑊W is...
