Introduction to multi-scale stochastic dynamics

Summary

This course develops a rigorous foundation in stochastic processes, limit theorems, and stochastic dynamics, with an emphasis on tools for analyzing systems across multiple scales.

Content

Keywords

Gaussian processes, self-similar processes, stationary processes, invariant measures, ergodicity, strong mixing,  limit theorems, Brownian motions and fractional Brownian motions,  rough paths,  stochastic dynamics,  stochastic differntial equations, rough differential equations.

Learning Prerequisites

Required courses

Required background knowledge:  Analysis I-IV, Probability.

Knowledge of the following are useful: stochactic integrals,   differntiale equations, Banach spaces, metric spaces.

Important concepts to start the course

Brownian motion, Stochastic Processes

Teaching methods

Weekly lectures and exercise sessions with assistant

Assessment methods

Oral

Supervision

Resources

Moodle Link

• https://go.epfl.ch/MATH-487