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Cramer's decomposition theorem within the continuation of distribution functions

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Stability Problems for Stochastic Models

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1233))

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Abstract

Continuing the papers [5] and [9] the author derives variants of Cramér's theorem which result if the corresponding integral equation is assumed to be valid only on a half line. The method is elementary the main tools being the simple but important lemmas of the Phragmén-Lindelöf theory. The method permits also to treat Linnik's factorization theorem.

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References

  1. Blank, N.M., and I.V. Ostrovskij (1981), Of functions of bounded variation close to the normal distribution function. Theory of operators in functional spaces and its applications, Kiev (russ.).

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  6. Rossberg, H.-J. (1985), The connection between limit theorems involving restricted convergence and the continuation theory of distribution functions. Statistics and Decisions, Second Supplement Issue, in print.

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  7. Rossberg, H.-J., B. Jesiak, and G. Siegel (1981), Continuation of distribution functions. In: Gani, J., and V.K. Rohatgi (eds.) Contributions to probability: A collection of papers dedicated to Eugene Lukacs. Academic Press, New York-London, 29–48.

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  8. Rossberg, H.-J., B. Jesiak, and G. Siegel (1985), Analytic methods of probability theory, Akademie-Verlag, Berlin.

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  9. Titov, A.N. (1981), On the determination of a convolution of equal distribution functions by its values given on a half line. Theory Prob. Appl. 26, 610–611, russ.

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Vladimir V. Kalashnikov Boyan Penkov Vladimir M. Zolotarev

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© 1987 Springer-Verlag

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Rossberg, HJ. (1987). Cramer's decomposition theorem within the continuation of distribution functions. In: Kalashnikov, V.V., Penkov, B., Zolotarev, V.M. (eds) Stability Problems for Stochastic Models. Lecture Notes in Mathematics, vol 1233. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072720

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  • DOI: https://doi.org/10.1007/BFb0072720

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-17204-8

  • Online ISBN: 978-3-540-47394-7

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