MVE565/MMA630 Computational methods for stochastic differential equations
This page contains the program of the course: lectures, exercise sessions and projects. Other information, such as learning outcomes, teachers, literature and examination, are in a separate course PM.
Program
The schedule of the course is in TimeEdit.
Lectures
Day | Sections | Content | Questions |
Slides & notes |
---|---|---|---|---|
20/1 | ([G] Chp. 1-3) | Introduction | ||
23/1 | [G] 4.1 - 4.2 | Brownian motion, Itô integral | Questions Lecture 2 | |
27/1 | [G] 4.2 - 4.3 | Itô integral, stochastic differential equations | Questions Lecture 3 | |
28/1 | [G] 4.3, 4.4 - 4.5 |
cont. SDE Feynman-Kac formulas |
Questions Lecture 4 | |
3/2 | [G] 4.4-4.5, 5.1 - 5.2 |
cont. Feynman-Kac Euler-Maruyama scheme, strong convergence |
Questions Lecture 5 | |
6/2 |
[G] 5.1 - 5.2 2 (new for you) |
Monte Carlo methods strong convergence |
Questions Lecture 6 | |
10/2 | [G] 5.3(-5.4), 6.1 |
Weak convergence statistical errors |
Questions Lecture 7 | |
11/2 | [G] 6.1-6.3 | (Multilevel) Monte Carlo | Questions Lecture 8 | |
17/2 |
[G] 6
|
Discussion Project 1 Repetition [G] (Multilevel Monte Carlo) |
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20/2 |
Cont. discussion Project 1 and repetition [G] Sobolev spaces |
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24/2 | Sobolev spaces and variational formulation, Gelfand triplet | Questions Lecture 11 | ||
27/2 | Variational formulation, discretization and matrix form | Questions Lecture 12 | ||
2/3 | [HRSW] 3.5-3.6 | Stability and error analysis | Questions Lecture 13 | |
5/3 | [HRSW] 4.3 | Localization (based on the given section) |
Recommended exercises
Hints on certain exercises: pdf
Day | Exercises |
---|---|
30/1 | 4.1-4.2 |
4/2 | 4.3-4.4 |
13/2 | 4.5,5.1 |
18/2 | 5.2-5.3 |
25/2 | 6.1-6.2 |
3/3 |
Projects
Two projects can be handed in for up to four bonus points per project on the ordinary exam. Reports are written and submitted individually.
Project 1: deadline February 17, 2020, 07:00
Project 2: deadline March 12, 2020, 07:00
Reference literature:
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[G] Emmanuel Gobet: Monte-Carlo Methods and Stochastic Processes: From Linear to Non-Linear, CRC, 2016
- [KP] Peter Kloeden, Eckhard Platen: Numerical Solutions of Stochastic Differential Equations, Springer, 1992
- [
- Learning MATLAB, Tobin A. Driscoll. Provides a brief introduction to Matlab to the one who already knows computer programming. Available as e-book from Chalmers library.
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Physical Modeling in MATLAB 3/E, Allen B. Downey
The book is free to download from the web. The book gives an introduction for those who have not programmed before. It covers basic MATLAB programming with a focus on modeling and simulation of physical systems.
Course summary:
Date | Details | Due |
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