Synergetics pp 69-103 | Cite as


How Far a Drunken Man Can Walk
  • Hermann Haken
Part of the Springer Series in Synergetics book series (SSSYN, volume 1)


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.


Brownian Movement Conditional Probability Markov Process Transition Rate Joint Probability 
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A Model of Brownian Motion

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The Random Walk Model and Its Master Equation

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

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

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The Master Equation

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

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Kirchhoff s Method of Solution of the Master Equation

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Theorems About Solutions of the Master Equation

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

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Copyright information

© Springer-Verlag Berlin Heidelberg 1978

Authors and Affiliations

  • Hermann Haken
    • 1
  1. 1.Institut für Theoretische PhysikUniversität StuttgartStuttgart 80Fed. Rep. of Germany

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