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TU Berlin

Inhalt des Dokuments

Stochastic Equations and Processes in Physics and Biology

Lupe

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 (PDF, 326,6 KB)
Lectures part 2 (PDF, 297,3 KB)

Tutorials

Tutorial 1 (PDF, 119,0 KB)
Tutorial 2 (PDF, 35,3 KB)

Zusatzinformationen / Extras