Stochastic methods for physics and biology, spring 2010
Stochastic methods for physics and biology, spring 2010
Lecturer
Stefan Geritz
Paolo Muratore-Ginanneschi
Scope
The aim of the course is to introduce the basic concepts of the theory of stochastic differential equations needed in applications (applied mathematics, physics and biology). In particular we will illustrate methods of qualitative, asymptotic and numerical analysis.
10 cu.
Type
Advanced studies.
Prerequisites
Lectures
Weeks 3-9 and 11-18, Monday 14-16 in room C124 and Friday 14-16 in room C123.
Easter holiday 1.-7.4.
First lecture: Friday, 22.01.2010
Lecture Notes
The lecture notes cover and sometimes integrate the material expounded in the lections. They also give bibliographic references for the same topics. For exercises please refer to the section below.
Lectures 1-10 | Lectures 10-20 |
---|---|
: Background of Probability | : Kolmogorov-Chentsov theorem |
: Bernoulli variables, Borel-Cantelli lemma | : White-noise |
: Limit theorems | : Ito integral |
: Martingales | : Ito and Stratonovich calculus |
: Numerical generation of random variables | : SDE, existence and uniqueness |
: Statistical tests | : Kolmogorov pair and diffusion |
: Fokker-Planck equation I | : Exit time statistics |
: Fokker-Planck equation II | : Girsanov formula |
: Brownian motion | : Numerical integration of SDE's |
: Karhunen-Loève representation | : Population dynamics |
Exams
There will be two options for taking the course. Passing an exam to be held after the end of the course, in
date to be agreed or working out a short project (recommended).
Bibliography
- L.C. Evans, "An Introduction to Stochastic Differential Equations", lecture notes.
- P. E. Kloeden, E. Platen, H. Schurz, "Numerical Solution Of Sde Through Computer Experiments", Springer (Universitext) (2003).
- N. Berglund, B. Gentz "Noise-Induced Phenomena in Slow-Fast Dynamical Systems. A Sample-Paths Approach", Springer (Probability and its Applications) (2005).
- D.J. Higham, "An algorithmic introduction to numerical simulation of stochastic differential equations" SIAM Review, Education Section, 43, 2001, 525-546. (Link to Higham's publications page.)
Book extended preview is available on line from google books
Registration
Did you forget to register? What to do.
Exercise groups
Group | Day | Time | Place | Instructor |
---|---|---|---|---|
1. | Wednesday | 16-18 | C124 |
|
Courseware
The codes below make use of the pgplot graphic library and of the GNU GSL
scientific library. You need to install these packages in order to use the codes as they are.
and its