Elements of Probability Theory

  • Heinz Parkus
Part of the International Centre for Mechanical Sciences book series (CISM, volume 9)


The abstract measure — theoretical development of probability theory during the last three decades, initiated by Kolmogorov [1], [2] is, for applications to physical problems, neither necessary nor even desirable. Therefore, no use is made of it in the following brief summary of basic definitions and formulas of probability theory.


Probability Theory Markov Process Random Process Poisson Process Random Function 


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  1. [1]
    A.N. Kolmogorov: Ueber die analytischen Methoden in der Wahrscheinlichkeitsrechnung. Math. Ann. 104 (1931),p. 415.CrossRefMATHMathSciNetGoogle Scholar
  2. [2]
    A.N. Kolmogorov: Grundbegriffe der Wahrscheinlich keitsrechnung. Ergeb. Math. und ihrer Grenzgeb. Bd. 2, No. 3, 1933.Google Scholar
  3. [3]
    R. von Mises: Wahrscheinlichkeitsrechnung. Deuticke. Wien 1931.Google Scholar
  4. [4]
    A. Papoulis: Probability, Random Variables and Stochastic Processes. McGraw-Hill Book Comp. New York 1965.MATHGoogle Scholar
  5. [5]
    E. Parzen: Modern Probability Theory and its Applications. Wiley. New York 1960.MATHGoogle Scholar
  6. [6]
    E. Parzen: Stochastic Processes. Holden-Day. San Francisco 1962.MATHGoogle Scholar
  7. [7]
    J. Heinhold und K.-W. Gaede: Ingenieur-Statistik. Oldenbourg-Verlag. München-Wien 1964.Google Scholar
  8. [8]
    A.A. Sweschnikow: Untersuchungsmethoden der Theorie der Zufallsfunktionen. Teubner. Leipzig 1965.MATHGoogle Scholar
  9. [9]
    W. Eberl: Einführung in die Stochastik. I. Teil, Wahrscheinlichkeitstheorie. Wiener Schwachstromwerke, Wien 1965.Google Scholar
  10. [10]
    M.F.M. Osborne: Reply to comments on Brownian motion in the stock market. Oper. Research 7 (1959), 807–811.CrossRefMathSciNetGoogle Scholar
  11. [11]
    E. Wax (editor): Selected Papers on Noise and Stochastic Processes. Dover Publications. New York 1954.MATHGoogle Scholar
  12. [12]
    A.H. Gray and T.K. Caughey: A controversy in prob lems involving random parametric excitation. J. Math. Phys. 44 (1965), 288.MATHGoogle Scholar

Copyright information

© Springer-Verlag Wien 1969

Authors and Affiliations

  • Heinz Parkus
    • 1
  1. 1.Technical University of ViennaAustria

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