Stochastic processes from deterministic dynamics

  • Christian Beck
Part I: Lectures
Part of the Lecture Notes in Physics book series (LNP, volume 457)


We deal with classes of smooth deterministic mappings that generate Brownian motion and Langevin processes in an appropriate scaling limit. We investigate the non-Gaussian corrections that occur if the scaling limit is not completely performed. We deal with higher-order correlation functions, and describe how to calculate probability densities in a perturbative way. As a physical application we describe a chaotic cascade model for fully developed turbulent flows. The slightly asymmetric non-Gaussian corrections of our model, produced by the underlying deterministic chaotic dynamics, come out in the same way as in various turbulence experiments. We also deal with possible applications of our approach in Euclidean quantum mechanics. The effects of a chaotic dynamics generating the Wiener process of the Feynman-Kac formula on a very small time scale are discussed.


Ground State Energy Wiener Process Velocity Difference Bernoulli Shift Small Time Scale 
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Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Christian Beck
    • 1
  1. 1.School of Mathematical Sciences Queen Mary and Westfield CollegeUniversity of LondonLondonEngland

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