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Stochastic Equations and Processes in Physics and Biology
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Lecture course in winter semester 2013 consisting of 8 lectures in total
Lecturer:
Dr. Andrey Pototsky
(Swinburne University of Technology, Melbourne)
Period:
November 18 - December 12, 2013
Day, time, and place
Mondays, 16:15 - 17:45 h, and
Thursdays, 14:15 - 15:45 h
in room ER 164 at TU Berlin.
Course Outline
- Probability and stochastic processes: general mathematical framework.
- Random walk and first passage time
- Auto-correlation function and the Wiener-Khinchin theorem.
- Computation of power spectral density for linear stochastic equations.
- The Wiener process and the diffusion equation.
- Basics of the Ito and Stratonovich stochastic calculus.
- The Fokker-Planck equation.
- Brownian Ratchets: general theory, examples involving asymptotic expansion
- The Fokker-Planck equation: eignefunction expansion and the linear response theory
- systems with interactions: from statistical physics to Density Functional Theory
Recommended literature:
- C. Gardiner, Stochastic Methods. A Handbook for the Natural and Social Sciences
- Hannes Risken, The Fokker-Planck Equation
- R.L. Stratonovich, Topics in the Theory of Random Noise
- William Feller, An Introduction to Probability Theory and its Applications
Lecture pdfs
Lectures part 1
Lectures part 2
Tutorials