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
Gaussian Measures, Gaussian stochastic processes, mixing and erdocity, ergodic theorems, averaging, diffusion and rough generation, slow/fast Stochastic differential equations, and possibly rough differential equations.
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
| Office hours | No |
| Assistant.e.s | Yes |
| Forum | No |
In the programs
- Semester: Fall
- Exam form: Oral (winter session)
- Subject examined: Introduction to multi-scale stochastic dynamics
- Courses: 3 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Fall
- Exam form: Oral (winter session)
- Subject examined: Introduction to multi-scale stochastic dynamics
- Courses: 3 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Fall
- Exam form: Oral (winter session)
- Subject examined: Introduction to multi-scale stochastic dynamics
- Courses: 3 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Fall
- Exam form: Oral (winter session)
- Subject examined: Introduction to multi-scale stochastic dynamics
- Courses: 3 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional