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.
Keywords
- Banach Space
- Central Limit Theorem
- Convex Body
- Separable Banach Space
- Partial Attraction
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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
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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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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-12295-1
Online ISBN: 978-3-540-39870-7
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