IMI-BAS BAS
 

BulDML at Institute of Mathematics and Informatics >
IMI >
IMI Periodicals >
Serdica Mathematical Journal >
1999 >
Volume 25 Number 3 >

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, 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.
URI: http://hdl.handle.net/10525/448
ISSN: 1310-6600
Appears in Collections:Volume 25 Number 3

Files in This Item:

File Description SizeFormat
sjm-vol25-num3-1999-p241-p256.pdf502.62 kBAdobe PDFView/Open

 



Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.

 

Valid XHTML 1.0!   Creative Commons License DSpace Software Copyright © 2002-2009  The DSpace Foundation - Feedback