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On the connections between weakly stable and pseudo-isotropic distributions

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  • Jasiulis, B.H.
  • Misiewicz, J.K.

Abstract

A random vector is weakly stable iff for all there exists a random variable [Theta] such that . This is equivalent (see Misiewicz et al. [Misiewicz, J.K., Oleszkiewicz, K., Urbanik, K., 2005. Classes of measures closed under mixing and convolution. Weak stability. Stud. Math. 167 (3), 195-213]) to the condition that for all random variables Q1,Q2 there exists a random variable [Theta] such that where are independent. Some of the weakly stable distributions turn out to be the extreme points for the class of pseudo-isotropic distributions, where the distribution is pseudo-isotropic if all its one-dimensional projections are the same up to a scale parameter. We show here that the scaling function for pseudo-isotropic distribution can define a generalized distribution iff it is an [alpha]-norm for some [alpha]>0.

Suggested Citation

  • Jasiulis, B.H. & Misiewicz, J.K., 2008. "On the connections between weakly stable and pseudo-isotropic distributions," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2751-2755, November.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:16:p:2751-2755
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    Cited by:

    1. Barbara H. Jasiulis, 2010. "Limit Property for Regular and Weak Generalized Convolution," Journal of Theoretical Probability, Springer, vol. 23(1), pages 315-327, March.
    2. Chr. Framstad, Nils, 2011. "Portfolio Separation with -symmetric and Psuedo-isotropic Distributions," Memorandum 12/2011, Oslo University, Department of Economics.

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