Introduction to multi-scale stochastic dynamics

Summary

This course introduces slow/fast systems and the mathematical tools used to derive effective equations governing their behaviour. Students will learn core concepts and techniques for rigorously analysing complex stochastic multi-scale systems.

Content

Keywords

slow/fast systems; stochastic processes with specific properties-- Markov, non-Markov processes, martingales, rough paths,  invariant measures; ergodicity;  Stochastic Differential Equations, functional central Limit theorems and fluctations;   averaging principle;  diffusion / rough creation, modern perspectives.

Learning Prerequisites

Required courses

Required background knowledge:  Analysis, Probability, Stochastic Processes, Measure and Integration, ODEs, PDEs, Metric spaces and Functional Analysis.

Important concepts to start the course

Brownian motion, Stochastic Processes in general, mode of convergence in probability theory, martingales, Markov property, invariant measures.

Learning Outcomes

By the end of the course, the student must be able to:

• Demonstrate thorough understanding of the topics covered.

Assessment methods

Oral

Resources

Moodle Link

• https://go.epfl.ch/MATH-487