TU Berlin

Graduiertenkolleg 1558Pototsky 2013

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Stochastic Equations and Processes in Physics and Biology


Lecture course in winter semester 2013 consisting of 8 lectures in total


Dr. Andrey Pototsky

(Swinburne University of Technology, Melbourne)


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


Tutorial 1
Tutorial 2



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