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).
Target group: Master students, PhD students
Prerequisites: Background in Mathematical Analysis
Basic knowledge of PDEs (Sobolev spaces, elliptic equations) and Probability
Evaluation: Presentations
Teaching format: Lectures
ECTS: 3 Year: 2022
Track segment(s):
Elective
Teacher(s):
Antonio Agresti Federico Cornalba
Teaching assistant(s):
If you want to enroll to this course, please click: REGISTER
- Teacher: Antonio Agresti
- Teacher: Federico Cornalba