JV: Stochastic Processes

Wiki

I set up a Wiki for

announcements
notes
publishing and discussing exercises
providing solutions

Topics

Probabilities. distributions, moments, cumulants
characteristic functions, Laplace-Legendre transformations

Random Processes. random walks, Lévy walks, anomalous transport
central limit theorem, Lévy distribution, large deviation theory

Markov processes. master equation, Kramers-Moyal expansion, Fokker-Planck equation
ergodicity, transport theory, first passage problems

Langevin dynamics. stochastic differential equations, Stratonovic and Ito calculus
Kramers problem, reactions coordinates, path of least action
stochastic thermodynamics, fluctuation relations, linear-response theory

Stochastic Thermodynamics. fluctuation relations, thermodynamic efficiency, linear-response theory

Background and Supporting Material for Lectures

I will use Python and Sage for numerical studies and visualization. The script files are notebooks that run interactively in Jupyter. Please store them on your computer, start Jupyter, and then open the notebook. The files contain fairly minimalistic explanations and comments. Feel free to add more comments and explanations, and return them to me.

As introductions to Python and Sage I recommend the books Steward: "Python for Scientists" and Zimmermann u.a.: "Computational Mathematics with SageMath".

I am working on a skript with more information on the course. The PDF-version of the first draft can be downloaded here. A gzip-compressed tar bundle that contains the PDF-file and Sage-Skripts with further illustrations and first homework assignments is available here.

Meetings

There will be a introductory session will meet an discuss about time slots for the lectures and the seminar.

on Tuesday, April 5
at 5pm
in ITP, SR 211

where we discuss about the course, and time slots for the lectures and the seminar.

Exams

There will be oral exams at the earliest opportunity after the end of the term.

Literature

     H. Haken      Synergetics. An Introduction      Springer 1983.

     an excellent introduction to key ideas from a physics perspective

     Feller An Introduction to Probability Theory and its Applications, Vol 1 Wiley 1968.

     an excellent introduction to key ideas from a mathematics perspective

     van Kampen Stochastic Processes in Physics and Chemistry Elsevier 1981

     a rich source for applications in physics, in particular of Master equations

specialized sources worth considering:

     Risken The Fokker-Planck Equation Springer 1989

     Gardiner Handbook of Stochastic Methods Springer 1985

     Redner A Guide to First-Passage Processes Cambridge 2001

visionary classical texts:

     Einstein      Investigations on the Theory of the Brownian Motion      Dover 1956

     Hill      Free Energy Transduction and Biochemical Cycle Kinetics      Dover 2005

Links

U. Behn Literature List (PDF) Links of Interest

Probabilities.	distributions, moments, cumulants characteristic functions, Laplace-Legendre transformations

Random Processes.	random walks, Lévy walks, anomalous transport central limit theorem, Lévy distribution, large deviation theory

Markov processes.	master equation, Kramers-Moyal expansion, Fokker-Planck equation ergodicity, transport theory, first passage problems

Langevin dynamics.	stochastic differential equations, Stratonovic and Ito calculus Kramers problem, reactions coordinates, path of least action stochastic thermodynamics, fluctuation relations, linear-response theory

Stochastic Thermodynamics.	fluctuation relations, thermodynamic efficiency, linear-response theory

	H. Haken	Synergetics. An Introduction	Springer 1983.
		an excellent introduction to key ideas from a physics perspective
	Feller	An Introduction to Probability Theory and its Applications, Vol 1	Wiley 1968.
		an excellent introduction to key ideas from a mathematics perspective
	van Kampen	Stochastic Processes in Physics and Chemistry	Elsevier 1981
		a rich source for applications in physics, in particular of Master equations
specialized sources worth considering:
	Risken	The Fokker-Planck Equation	Springer 1989
	Gardiner	Handbook of Stochastic Methods	Springer 1985
	Redner	A Guide to First-Passage Processes	Cambridge 2001
visionary classical texts:
	Einstein	Investigations on the Theory of the Brownian Motion	Dover 1956
	Hill	Free Energy Transduction and Biochemical Cycle Kinetics	Dover 2005

SoSe2022. Stochastic Processes