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Invariance principles for generalized domains of semistable attraction

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  • Wang, Wensheng

Abstract

Let X,X1,X2,… be independent and identically distributed Rd-valued random vectors and assume X belongs to the generalized domain of attraction of some operator semistable law without normal component. Then without changing its distribution, one can redefine the sequence on a new probability space such that the properly affine normalized partial sums converge in probability and consequently even in Lp (for some p>0) to the corresponding operator semistable Lévy motion.

Suggested Citation

  • Wang, Wensheng, 2014. "Invariance principles for generalized domains of semistable attraction," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 1-17.
    • Handle: RePEc:eee:spapps:v:124:y:2014:i:1:p:1-17
    DOI: 10.1016/j.spa.2013.07.004
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    References listed on IDEAS

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    1. Scheffler, Hans-Peter, 1995. "Moments of measures attracted to operator semi-stable laws," Statistics & Probability Letters, Elsevier, vol. 24(3), pages 187-192, August.
    2. Hudson, William N. & Veeh, Jerry Alan & Weiner, Daniel Charles, 1988. "Moments of distributions attracted to operator-stable laws," Journal of Multivariate Analysis, Elsevier, vol. 24(1), pages 1-10, January.
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    Cited by:

    1. Wensheng Wang, 2017. "Large Deviations for Sums of Random Vectors Attracted to Operator Semi-Stable Laws," Journal of Theoretical Probability, Springer, vol. 30(1), pages 64-84, March.

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