Abstract
It is shown that, contrary to the finite dimensional situation, for every infinite dimensional Banach space B there exists a B-valued r.v. X in the domain of partial attraction of only one type of (non-degenerate, stable) laws, but not in its domain of attraction.
Partially supported by a National Science Foundation Grant.
On leave at Texas A&M University for '82-'83 academic year.
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References
Araujo, A. and Giné, E. (1980). The Central Limit Theorem. Wiley, New York.
Dvoretzky, A. (1960). Some results on convex bodies and Banach spaces. Proc.Int.Symp. on Linear Spaces, Jerusalem 1960. Jerusalem Academic Press, Jerusalem, pp. 123–160.
Giné, E. (1980). Domains of partial attraction in several dimensions. Ann.Inst.Poincaré XVI, 87–100. Correction: Ann.Inst.Poincaré XVII, 143–145.
Jain, N. and Orey, S. (1980). Domains of partial attraction and tightness conditions. Ann. Probability 8, 584–599.
Morrell, J.S. and Retherford, J.R. (1972). p-trivial Banach spaces. Studia Math. 43, 1–25.
Pisier, G. and Zinn, J. (1978). On the limit theorems for random variables with values in Lp, p ≥ 2. Z.Wahrscheinlichkeitstheorie verw.Geb. 41, 289–304.
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© 1983 Springer-Verlag
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Giné, E. (1983). A counterexample on domains of partial attraction in banach spaces. In: Beck, A., Jacobs, K. (eds) Probability in Banach Spaces IV. Lecture Notes in Mathematics, vol 990. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0064266
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DOI: https://doi.org/10.1007/BFb0064266
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