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Chance

How Far a Drunken Man Can Walk

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Synergetics

Part of the book series: Springer Series in Synergetics ((SSSYN,volume 1))

Abstract

While in Chapter 2 we dealt with a fixed probability measure, we now study stochastic processes in which the probability measure changes with time. We first treat models of Brownian movement as example for a completely stochastic motion. We then show how further and further constraints, for example in the frame of a master equation, render the stochastic process a more and more deterministic process.

This Chapter 4, and Chapter 5, are of equal importance for what follows. Since Chapter 4 is somewhat more difficult to read, students may also first read 5 and then 4. On the other hand, Chapter 4 continues directly the line of thought of Chapters 2 and 3. In both cases, chapters with an asterisk in the heading may be omitted during a first reading.

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References

A Model of Brownian Motion

  • N. Wax, ed.: Selected Papers on Noise and Statistical Processes (Dover Publ. Inc., New York 1954) with articles by S. Chandrasekhar, G. E. Uhlenbeck and L. S. Ornstein, Ming Chen Wang and G. E. Uhlenbeck, M. Kac

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The Random Walk Model and Its Master Equation

Joint Probability and Paths. Markov Processes. The Chapman-Kolmogorov Equation. Path Integrals

How to Use Joint Probabilities. Moments. Characteristic Function. Gaussian Processes

The Master Equation

Exact Stationary Solution of the Master Equation for Systems in Detailed Balance

Kirchhoff s Method of Solution of the Master Equation

Theorems About Solutions of the Master Equation

The Meaning of Random Processes. Stationary State, Fluctuations, Recurrence Time

  • P. and T. Ehrenfest: Phys. Z. 8, 311 (1907)

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  • A. Münster: In Encyclopedia of Physics, ed. by S. Flügge, Vol. III/2; Principles of Thermodynamics and Statistics (Springer, Berlin-Göttingen-Heidelberg 1959)

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© 1983 Springer-Verlag Berlin Heidelberg

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Haken, H. (1983). Chance. In: Synergetics. Springer Series in Synergetics, vol 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-88338-5_4

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  • DOI: https://doi.org/10.1007/978-3-642-88338-5_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-88340-8

  • Online ISBN: 978-3-642-88338-5

  • eBook Packages: Springer Book Archive

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