An Introduction to Stochastic Equations: Analysis and Numerics

This course is aimed at giving a general overview of some basic results concerning the analysis and numerics for stochastic (partial) differential equations, usually referred to as S(P)DEs. Analysis section (roughly 50% of the course) Provisional goals: i) to acquire familiarity with Itô calculus in Hilbert spaces; ii) to provide basic notions of the variational theory of SPDEs, including standard examples (such as, e.g., stochastic heat equation, stochastic Navier-Stokes equations). Numerics section (roughly 50% of the course) Provisional goals: i) to recall basic numerical notions for deterministic partial differential equations; ii) to introduce basic numerical integration methods for stochastic equations; iii) to explain in detail a few selected applications (such as, e.g., stochastic heat equation, equations of fluctuating hydrodynamics describing large-scale particle systems).