Taylor Expansions for Stochastic Partial Differential Equations
Seminar Room 1, Newton Institute
Taylor expansions are a fundamental and repeatedly used means of approximation in mathematics, in particular in numerical analysis.
While local approximations and local expansions of a function yield a better understanding of local properties of such a function from a theoretical point of view, many numerical schemes for various types of differential equations are based on Taylor expansions of the solution of such an equation. In this talk, we present Taylor expansions of the solution of a stochastic partial differential equation (SPDE) of evolutionary type and their first applications to numerical analysis. The key instruments for deriving such Taylor expansions are the fundamental theorem of calculus for Banach space valued functions and an appropriate recursion technique.