Welcome to the lecture wiki Stochastic Processes (winter term 2015/16)

General

Lecture: Felix Höfling
Problems: Jan-Hendrik Prinz, Felix Höfling
Language: English
SWS/Credits: 4+2 / 10 LP
Students: M.Sc. Mathematics, M.Sc. Physics

Dates

	Date	Time	Location	room
Lecture	Tuesdays	2 p.m.	Arnimallee 3-5	lecture hall 001
Lecture	Wednesdays	2 p.m.	Arnimallee 3-5	lecture hall 001
Problem class	Wednesdays	4 p.m.	Arnimallee 6	seminar room 009

Content

The course provides an introduction to stochastic processes with applications in physics and chemistry. We will develop the mathematical theory in the language of modern probability theory, mostly following the book by Øksendal. The results are then applied to diffusion problems and non-Markovian transport (as in heterogeneous fluids), with the Brownian motion of a colloidal particle serving as paradigmatic example. Further, we will discuss the modelling of chemical reactions, the derivation of stochastic equations of motion from a many-particle Liouville dynamics, and recent developments in non-equilibrium physics.

Script

1. Stochastic processes and correlation functions [Øksendal]
   13/10 14/10 20/10 21/10 27/10 28/10 3/11
2. Molecular transport phenomena [Hansen/McDonald]
   4/11 10/11 11/11 17/11 18/11
3. Stochastic differential equations [Øksendal]
   18/11 24/11 25/11 01/12 02/12 08/12
4. Markov processes [van Kampen, Gardiner, Dynkin]
   09/12 15/12 16/12 05/01 06/01 12/01 13/01 19/01 20/01
5. Statistical mechanics [Kubo]
   26/01 27/01 02/02 03/02 09/02 10/02

Problem sheets

• revision: chapters 1-3 4-5
• problem sheet #1 (21/10)
• problem sheet #2 (28/10)
• problem sheet #3 (04/11)
• problem sheet #4 (11/11)
• problem sheet #5 (18/11)
• problem sheet #6 (25/11)
• problem sheet #7 (02/12)
• problem sheet #8 (09/12)
• problem sheet #9 (16/12)
• problem sheet #10 (06/01)
• problem sheet #11 (13/01)
• problem sheet #12 (20/01)
• problem sheet #13 (27/01)
• problem sheet #14 (03/02)
• a problem on the Tonks gas (with solution)

Literature (alphabetic order)

• Dynkin: Markov processes (Springer, 1965)
• Gardiner: Handbook of Stochastic Methods (Springer, 2004)
• Hansen, McDonald: Theory of Simple Liquids (Academic, 2006)
• Kubo, Toda, Hashitsume: Statistical Physics II (Springer, 1998)
• Øksendal: Stochastic Differential Equations (Springer, 2010)
• Paul, Baschnagel: Stochastic Processes (Springer, 2013)
• van Kampen: Stochastic Processes in Physics and Chemistry (Elsevier, 2007)

Contact

Name	Consultation Hour	Mail
Prof. Dr. Felix Höfling	appointment by e-mail	f.hoefling[at]fu-berlin.de
Dr. Jan-Hendrik Prinz	appointment by e-mail	jan-hendrik.prinz[at]fu-berlin.de

The material is accessed with