MATH-485 / 5 crédits

Enseignant: Hairer Martin

Langue: Anglais


Summary

Stochastic PDEs are used to model systems that are spatially extended and include a random component. This course gives an introduction to this topic, including some Gaussian measure theory and some analytic semigroup theory.

Content

Keywords

probability, partial differential equations, semigroups, Gaussian measures

Learning Prerequisites

Required courses

Analysis I-IV

Probability

Recommended courses

Measure and integration

Probability theory

Important concepts to start the course

Basic concepts in probability theory

Basic properties of Hilbert and Banch spaces

Teaching methods

Weekly lectures (on blackboard) and exercise sessions with assistant

Expected student activities

Attending the lectures and solving the exercises

Assessment methods

Oral exam

Supervision

Office hours No
Assistants Yes
Forum No

Resources

Virtual desktop infrastructure (VDI)

No

Bibliography

G. DA PRATO and J. ZABCZYK. Stochastic equations in infinite dimensions, vol. 44 of Encyclopedia of Mathematics and its Applications. Cambridge University Press, Cambridge, 1992.

A. LUNARDI. Analytic semigroups and optimal regularity in parabolic problems. Progress in Nonlinear Differential Equations and their Applications, 16. Birkhäuser Verlag, Basel, 1995.

V. I. BOGACHEV. Gaussian measures, vol. 62 of Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI, 1998.

P. BILLINGSLEY. Convergence of probability measures. John Wiley & Sons Inc., New York, 1968.

K. YOSIDA. Functional analysis. Classics in Mathematics. Springer-Verlag, Berlin, 1995. Reprint of the sixth (1980) edition.

Ressources en bibliothèque

Notes/Handbook

The lecture will mainly follow the notes available at https://www.hairer.org/notes/SPDEs.pdf, but might cover additional material if time permits.

Dans les plans d'études

  • Semestre: Printemps
  • Forme de l'examen: Oral (session d'été)
  • Matière examinée: Introduction to stochastic PDEs
  • Cours: 3 Heure(s) hebdo x 14 semaines
  • Exercices: 2 Heure(s) hebdo x 14 semaines

Semaine de référence

 LuMaMeJeVe
8-9  MAA331MAA331 
9-10  MAA331 
10-11    
11-12     
12-13     
13-14     
14-15     
15-16     
16-17     
17-18     
18-19     
19-20     
20-21     
21-22     

Mercredi, 8h - 10h: Cours MAA331

Jeudi, 8h - 9h: Cours MAA331

Jeudi, 9h - 11h: Exercice, TP MAA331