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Analytical Methods in Probability Theory

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Transactions of the Tenth Prague Conference

Part of the book series: Czechoslovak Academy of Sciences ((TPCI,volume 10A-B))

Abstract

An analogue of the method of characteristic functions for generalized convolutions is discussed. Moreover, the set of weak characteristic functions is described in terms of stable distributions. Finally, some applications to analysis are mentioned.

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References

  • Bingham N.H. (1971): Factorization theory and domains of attraction for generalized convolution algebras. In: Proc, London Math, Soc. 23, 16–30.

    Article  MathSciNet  MATH  Google Scholar 

  • Bingham N.H. (1984): On a theorem of Kłosowska about generalized convolutions. In: Colloq. Math. 48, 117–125.

    MathSciNet  MATH  Google Scholar 

  • Jajte R. (1976): Quasi-stable measures in generalized convolution algebras. In: Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 24, 505–511.

    MathSciNet  MATH  Google Scholar 

  • Jajte R. (1977): Quasi-stable measures in generalized convolution algebras II. In: Bull. Acad, Polon. Sci. Sér. Sci. Math. Astronom. Phys. 25, 67–72.

    MathSciNet  MATH  Google Scholar 

  • Jurek Z.J. (1981): Some characterizations of the class L in generalized convolution algebras. In: Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 29, 409–415.

    MathSciNet  MATH  Google Scholar 

  • Jurek Z.J. (1985): Limit distributions in generalized convolution algebras. In: Probab. Math. Statistics. 5, 113–135.

    MathSciNet  MATH  Google Scholar 

  • Kendall D.G. (1974): Foundations of a theory of random sets. In: Stochastic geometry (ed. E.F. Harding and D.G, Kendall ), Wiley, 322–376

    Google Scholar 

  • Kingman J.F. (1962): Random walks with spherical symmetry. In: Colloq. Comb. Methods in Prob. Theory, Aarhus, 40–46.

    Google Scholar 

  • Klosowska M. (1977): On the domain of attraction for generalized convolution algebras. In: Rev, Roum, Math. Pures et Appl. 22, 669–677.

    MATH  Google Scholar 

  • Kucharczak J. and Urbanik K. (1987): Transformations preserving weak stability. In: Bull. Pol. Acad: Math, (in print).

    Google Scholar 

  • Urbanik K. (1964): Generalized convolutions. In: Studia Math, 23, 217–245.

    MathSciNet  MATH  Google Scholar 

  • Urbanik K. (1973): Generalized convolutions II. In: Studia Math. 45, 57–70.

    MathSciNet  MATH  Google Scholar 

  • Urbanik K. (1984): Generalized convolutions III, In: Studia Math. 80, 167–189.

    MathSciNet  MATH  Google Scholar 

  • Urbanik K. (1985): Limit behaviour of medians. In: Bull. Pol. Acad: Math. 33, 413–419.

    MathSciNet  Google Scholar 

  • (1986): Generalized convolutions IV, In: Studia Math. 83, 57–95.

    MathSciNet  MATH  Google Scholar 

  • Vol’kovich V.E, (1984)Multidimensional B-stable distributions and realizations of generalized convolutions. In: Problems of Stability of Stochastic Models, 40–54 (in Russian).

    Google Scholar 

  • Zolotarev V.M. (1983): One-dimensional stable distributions, Nauka, (in Russian). Wrocław University, Institute of Mathematics PI, Grunwaldzki 2/4, 50–384 Wrocław Poland

    Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics, Wrocław University, Pl, Grunwaldzki 2/4, Wrocław, Poland, 50-384

    Kazimierz Urbanik

Authors
  1. Kazimierz Urbanik
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Jan Ámos Višek

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© 1988 Academia, Publishing House of the Czechoslovak Academy of Sciences, Prague

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Urbanik, K. (1988). Analytical Methods in Probability Theory. In: Višek, J.Á. (eds) Transactions of the Tenth Prague Conference. Czechoslovak Academy of Sciences, vol 10A-B. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3859-5_11

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  • DOI: https://doi.org/10.1007/978-94-009-3859-5_11

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-8216-7

  • Online ISBN: 978-94-009-3859-5

  • eBook Packages: Springer Book Archive

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