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Weak Limits for Multivariate Random Sums

✍ Scribed by Tomasz J Kozubowski; Anna K Panorska

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 314 KB
Volume: 67
Category: Article
ISSN: 0047-259X
DOI: 10.1006/jmva.1998.1768

No coin nor oath required. For personal study only.

✦ Synopsis

Let [X i , i 1] be a sequence of i.i.d. random vectors in R d , and let & p , 0< p<1, be a positive, integer valued random variable, independent of X i s. The &-stable distributions are the weak limits of properly normalized random sums & p i=1 X i , as & p w Ä P and p& p w Ä d &. We study the properties of &-stable laws through their representation via stable laws. In particular, we estimate their tail probabilities and provide conditions for finiteness of their moments.

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