Stable measures and central limit theorems in spaces of stable type
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- by Michael B. Marcus and Wojbor A. Woyczyński PDF
- Trans. Amer. Math. Soc. 251 (1979), 71-102 Request permission
Abstract:
Let X be a symmetric random variable with values in a quasinormed linear space E. X satisfies the central limit theorem on E with index p, $0 < p \leqslant 2$, if $\mathcal {L}{n^{ - 1/p}}({X_1} + \cdots + {{\text {X}}_n}))$ converges weakly to some probability measure on E. Hoffman-Jorgensen and Pisier have shown that Banach spaces of stable type 2 provide a natural environment for the central limit theorem with index $p = 2$. In this paper we show that, for $0 < p < 2$, quasi-normed linear spaces of stable type p provide a natural environment for the central limit theorem with index p. A similar result holds also for the weak law of large numbers with index p.References
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Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 251 (1979), 71-102
- MSC: Primary 60B12; Secondary 60E07
- DOI: https://doi.org/10.1090/S0002-9947-1979-0531970-2
- MathSciNet review: 531970