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Normal and degenerate convergences of random sums

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1412)

Keywords

  • Central Limit Theorem
  • Weak Convergence
  • Independent Random Variable
  • Weak Limit
  • Divisible Distribution

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References

  1. Gnedenko B.V., Kolmogorov A.N. Limit Distributions for Sums of Independent Random Variables. Moscow, Leningrad, 1949, 264 p. (in Russian).

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  2. Zolotarev V.M. Modern Theory of Summation of Independent Random Variables.. Moscow, Nauka, 1988, 415 p. (in Russian).

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  3. Loéve M. Probability Theory. Izd. Inostr. Lit., Moscow, 1968, 719 p. (in Russian).

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  4. Kruglov V.M. A characterization of a class of infinitely divisible distributions in a Hilbert space.-Mat.Zametki, 1974, 16, N 5, 777–782 (in Russian).

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  5. Szász D. Limit theorems for the distributions of the sums of a random number of random variables.-Ann.Math.Stat., 1972, 43, N 66, 1902–1913.

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© 1989 Springer-Verlag

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Kruglov, V.M. (1989). Normal and degenerate convergences of random sums. In: Kalashnikov, V.V., Zolotarev, V.M. (eds) Stability Problems for Stochastic Models. Lecture Notes in Mathematics, vol 1412. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0084170

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  • DOI: https://doi.org/10.1007/BFb0084170

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51948-5

  • Online ISBN: 978-3-540-46863-9

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