Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/448

 Title: Geometric Stable Laws Through Series Representations Authors: Kozubowski, TomaszPodgórski, Krzysztof Keywords: Geometric CompoundInvariance PrincipleLinnik DistributionMittag-Leffler DistributionRandom SumStable DistributionStochastic 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. URI: http://hdl.handle.net/10525/448 ISSN: 1310-6600 Appears in Collections: Volume 25 Number 3

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