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Title: Geometric Stable Laws Through Series Representations
Authors: Kozubowski, Tomasz
Podgórski, Krzysztof
Keywords: Geometric Compound
Invariance Principle
Linnik Distribution
Mittag-Leffler Distribution
Random Sum
Stable Distribution
Stochastic Integral
Issue Date: 1999
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 25, No 3, (1999), 241p-256p
Abstract: Let (Xi ) be a sequence of i.i.d. random variables, and let N be a geometric random variable independent of (Xi ). Geometric stable distributions are weak limits of (normalized) geometric compounds, SN = X1 + · · · + XN , when the mean of N converges to infinity. By an appropriate representation of the individual summands in SN we obtain series representation of the limiting geometric stable distribution. In addition, we study the asymptotic behavior of the partial sum process SN (t) = ⅀( i=1 ... [N t] ) Xi , and derive series representations of the limiting geometric stable process and the corresponding stochastic integral. We also obtain strong invariance principles for stable and geometric stable laws.
ISSN: 1310-6600
Appears in Collections:Volume 25 Number 3

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