On the Convergence of Distributions of Random Sums ofIndependent Random Variables to Stable Laws

Abstract

Previous article Next article On the Convergence of Distributions of Random Sums ofIndependent Random Variables to Stable LawsV. Yu. KorolevV. Yu. Korolevhttps://doi.org/10.1137/S0040585X97976544PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractThe paper gives the necessary and sufficient conditions for convergence of distributions of random sums of independent random variables to strictly stable laws.[1] Google Scholar[2] V. Yu. Korolev, Convergence of random sequences with independent random indices, Theory Probab. Appl., 39 (1994), pp. 282–297. tba TPRBAU 0040-585X Theor. Probab. Appl. LinkGoogle Scholar[3] Google ScholarKeywordsstable lawsLindeberg conditionrandom sums Previous article Next article FiguresRelatedReferencesCited byDetails Multivariate Scale-Mixed Stable Distributions and Related Limit Theorems8 May 2020 | Mathematics, Vol. 8, No. 5 Cross Ref From Asymptotic Normality to Heavy-Tailedness via Limit Theorems for Random Sums and Statistics with Random Sample Sizes15 April 2020 Cross Ref Some functional limit theorems for compound Cox processes Cross Ref Application of Compound Cox Processes In Modeling Order Flows with Non-Homogeneous IntensitiesSSRN Electronic Journal Cross Ref Modeling High-Frequency Order Flow Imbalance by Functional Limit Theorems for Two-Sided Risk ProcessesSSRN Electronic Journal Cross Ref On Convergence of Distributions of Compound Cox Processes to Stable LawsV. Yu. Korolev25 July 2006 | Theory of Probability & Its Applications, Vol. 43, No. 4AbstractPDF (119 KB) Volume 42, Issue 4| 1998Theory of Probability & Its Applications History Published online:17 February 2012 InformationCopyright © 1998 Society for Industrial and Applied MathematicsKeywordsstable lawsLindeberg conditionrandom sumsPDF Download Article & Publication DataArticle DOI:10.1137/S0040585X97976544Article page range:pp. 695-696ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics