Stochastic Processes and Their Applications in Modeling

for questions mailto:freund@icbm.uni-oldenburg.de                              return to homepage

Keywords:

  • Brownian motion: from pollen grains to nano robots (an introduction)
  • a primer on probability theory and statistics
  • the origin of noise and its characterization ("The Color of Noise")
  • Wiener process and diffusion
  • Markov process, Langevin and Fokker-Planck description
  • stochastic integration: Stratonovich vs. Ito
  • birth and death processes: master equation (population dynamics)
  • renewal and point process (neuronal spikes)
  • super and subdiffusion: Levy flights, Continuous Time Random Walks (biological motion)
  • externally driven processes (nonlinear amplifiers, filters, and sensors)
  • noise-induced phenomena (stochastic resonance, Brownian motors, etc.)

References:

  1. C. W. Gardiner: Handbook of Stochastic Methods: For Physics, Chemistry and the Natural Sciences, (Springer, Berlin, 1997).
  2. N. G. van Kampen: Stochastic Processes in Physics and Chemistry, (North-Holland, Amsterdam,1992).
  3. H. Risken: The Fokker-Planck Equation, (Springer, Berlin, 1989).
  4. J. Honerkamp: Stochastic Dynamical Systems, (Wiley-VCH, New York, 1994).
  5. J. A. Freund and T. Pöschel: Stochastic Processes in Physics, Chemistry, and Biology, (Springer, Berlin, 2000).
  6. L. Schimansky-Geier and T. Pöschel: Stochastic Dynamics, (Springer, Berlin, 1997).

           
Revised 4.14.04