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On the central limit theorem in Banach spaces

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  • de Araujo, Aloisio Pessoa

Abstract

It is shown, with the use of a concentration inequality of LeCam, that associated with an infinitely divisible random variable with values in a separable Banach space there is a Lévy-Khintchine formula. A partial converse of this fact is also proved. Relations between the continuity of the compound Poisson and the Gaussian variables associated with a Lévy measure are studied. A central limit theorem is obtained and examples are given.

Suggested Citation

  • de Araujo, Aloisio Pessoa, 1978. "On the central limit theorem in Banach spaces," Journal of Multivariate Analysis, Elsevier, vol. 8(4), pages 598-613, December.
    • Handle: RePEc:eee:jmvana:v:8:y:1978:i:4:p:598-613
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    Cited by:

    1. Jim Kuelbs & Joel Zinn, 2008. "Another View of the CLT in Banach Spaces," Journal of Theoretical Probability, Springer, vol. 21(4), pages 982-1029, December.
    2. Misiewicz, Jolanta K., 1995. "Infinite divisibility of sub-stable processes. Part I. geometry of sub-spaces of L[alpha]-space," Stochastic Processes and their Applications, Elsevier, vol. 56(1), pages 101-116, March.
    3. Dede, Sophie, 2009. "An empirical Central Limit Theorem in for stationary sequences," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3494-3515, October.
    4. Schmuland, Byron & Sun, Wei, 2001. "On the equation [mu]t+s=[mu]s*Ts[mu]t," Statistics & Probability Letters, Elsevier, vol. 52(2), pages 183-188, April.

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