Probability Theory

  • Hannes Risken
Part of the Springer Series in Synergetics book series (SSSYN, volume 18)


In this chapter we recapitulate some of the basic ideas and conceptions of probability theory needed to unterstand the other chapters. Though there are many text books on probability theory [2.1 – 6], a selection of basic ideas and concepts of probability theory in a simplified form may be in order for the reader not very familiar with probability theory.


Probability Density Characteristic Function Probability Theory Markov Process Inverse Fourier Transform 
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  1. 2.1
    R. von Mises: Mathematical Theory of Probability and Statistics (Academic, New York 1964)zbMATHGoogle Scholar
  2. 2.2
    B. W. Gnedenko: Lehrbuch der Wahrscheinlichkeitsrechnung (Akademie, Berlin 1957)Google Scholar
  3. 2.3
    W. Feller: An Introduction to Probability Theory and its Applications, Vols. 1 and 2 (Wiley, New York 1968 and 1971)Google Scholar
  4. 2.4
    Yu. V. Prohorov, Yu. A. Rozanov: Probability Theory, Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen, Bd. 157 (Springer, Berlin, Heidelberg, New York 1968)Google Scholar
  5. 2.5
    M. Loève: Probability Theory. Vols. 1 and 2, Graduate Texts Math. (Springer, New York, Heidelberg, Berlin 1977 and 1978)Google Scholar
  6. 2.6
    J. L. Doob: Stochastic Processes (Wiley, New York 1953)zbMATHGoogle Scholar
  7. 2.7
    J. D. Jackson: Classical Electrodynamics (Wiley, New York 1962) p. 4Google Scholar
  8. 2.8
    T. Muir: A Treatise on the Theory of Determinants (Dover, New York 1960) p. 719Google Scholar
  9. 2.9
    P. Hänggi, P. Talkner: J. Stat. Phys. 22, 65 (1980)ADSCrossRefGoogle Scholar
  10. 2.10
    S. O. Rice: Mathematical Analysis of Random Noise, in Selected Papers on Noise and Stochastic Processes, ed. by N. Wax (Dover, New York 1954) p. 133Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  • Hannes Risken
    • 1
  1. 1.Abteilung für Theoretische PhysikUniversität UlmUlmFed. Rep. of Germany

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