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Domains of Semi-Stable Attraction of Nonnormal Semi-Stable Laws

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  • Scheffler, H. P.

Abstract

A sequence of independent, identically distributed random vectors X1, X2, ... is said to belong to the -normed domain of semi-stable attraction of a random vector Y if there exist diagonal matrices An, constant vectors bn and a sequence (kn)n of natural numbers with kn [upwards double arrow] [infinity] and kn+1/kn --> c >= 1 such that An(X1 + · · · + Xkn) + bn converges in distribution to Y. The limit law Y is then called semi-stable. We present a simple, necessary, and sufficient condition for the existence of such An, bn, and kn in the case where Y has no normal component. Furthermore we prove some moment conditions for random vectors belonging to the -normed domain of semi-stable attraction of Y.

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  • Scheffler, H. P., 1994. "Domains of Semi-Stable Attraction of Nonnormal Semi-Stable Laws," Journal of Multivariate Analysis, Elsevier, vol. 51(2), pages 432-444, November.
    • Handle: RePEc:eee:jmvana:v:51:y:1994:i:2:p:432-444
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    Cited by:

    1. Mark M. Meerschaert & Hans-Peter Scheffler, 1997. "Spectral Decomposition for Generalized Domains of Semistable Attraction," Journal of Theoretical Probability, Springer, vol. 10(1), pages 51-71, January.
    2. Scheffler, Hans-Peter, 1995. "Moments of measures attracted to operator semi-stable laws," Statistics & Probability Letters, Elsevier, vol. 24(3), pages 187-192, August.
    3. Meerschaert, Mark M. & Scheffler, Hans-Peter, 1997. "The structure of generalized domains of semistable attraction," Statistics & Probability Letters, Elsevier, vol. 33(4), pages 367-372, May.

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