Stochastic processes in physics

Diplome(s)
Lieu
ENS-PSL
Automne - Hiver
Niveau Master 1 3 ECTS - En anglais
Enseignant(s) Massimo Vergassola ( ENS-PSL CNRS )
Chargé(s) de TD Marylou GABRIE ( ENS-PSL )
Contact - Secrétariat de l’enseignement

The course provides an introduction to stochastic processes with attention paid both to general methods and the diverse applications to physics and natural phenomena.

Programme

Lectures will combine in-depth analysis of a given method/equation and its applications to various natural phenomena. The topics will be selected yearly from the below list :

  1. Markov processes and Langevin equation 
  2. Brownian motion and Black-Scholes equation
  3. Continuous processes and Fokker-Planck equation
  4. Jump processes, master equation and Lévy processes
  5. First passage problems
  6. Stochastic differential equations 
  7. Residence times and Feynmann-Kac formula
  8. Fluctuations theorems and stochastic thermodynamics 
Evaluation

The final grade will be based on a combination of in-class participation (20%), results of the homework (30%) and the final exam (50%)

Prerequisites

Some background in probability is welcome but not necessary