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Limit theorems for random sums of independent random variables

Part of the Lecture Notes in Mathematics book series (LNM,volume 1546)

Keywords

  • Natural Number
  • Weak Convergence
  • Independent Random Variable
  • Independent Increment
  • Random Index

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References

  1. H. Robbins, The asymptotic distribution of the sum of a random number of random variables, Bull. Amer. Math. Soc., 54 (1948), pp. 1151–1161.

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  2. B. V. Gnedenko and H. Fahim, On a transfer theorem, Dokl. AN SSSR, 187 (1969), pp. 15–17. (In Russian.)

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  3. D. Szász, On the classes of limit ditributions for sums of a random number of identically distbuted random variables, Probab. Theory. Appl., 17 (1972), pp. 424–439.

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  4. D. Szász, Limit theorems for the distributions of the sums of a random number of random variables, Ann. Math. Stat., 43 (1972), pp. 1902–1913.

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  5. V. M. Kruglov and V. Yu. Korolev, Limit Theorems for Random Sums, Mosc. St. Univ. Publ., Moscow, 1990. (In Russian.)

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  6. J. L. Doob, Stochastic Processes, Wiley, New York, 1953.

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  7. M. Loéve, Probability Theory, Van Nostrand, Princeton, 1963.

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  8. B. V. Gnedenko and A. N. Kolmogorov, Limit Distributions for Sums of Independent Random Variables, Addison-Wesley, Reading, Massachusets, 1968.

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© 1993 Springer-Verlag

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Korolev, V., Kruglov, V.M. (1993). Limit theorems for random sums of independent random variables. In: Kalashnikov, V.V., Zolatarev, V.M. (eds) Stability Problems for Stochastic Models. Lecture Notes in Mathematics, vol 1546. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0084486

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  • DOI: https://doi.org/10.1007/BFb0084486

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  • Print ISBN: 978-3-540-56744-8

  • Online ISBN: 978-3-540-47645-0

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