 Conditional convergence to infinitely divisible distributions with finite varianceJérôme Dedecker and Sana Louhichi Stochastic Processes and their Applications, 2005, vol. 115, issue 5, 737-768 Abstract: We obtain new conditions for partial sums of an array with stationary rows to converge to a mixture of infinitely divisible distributions with finite variance. More precisely, we show that these conditions are necessary and sufficient to obtain conditional convergence. If the underlying [sigma]-algebras are nested, conditional convergence implies stable convergence in the sense of Rényi. From this general result we derive new criteria expressed in terms of conditional expectations, which can be checked for many processes such as m-conditionally centered arrays or mixing arrays. When it is relevant, we establish the weak convergence of partial sum processes to a mixture of Lévy processes in the space of cadlag functions equipped with Skorohod's topology. The cases of Wiener processes, Poisson processes and Bernoulli distributed variables are studied in detail. Keywords: Infinitely; divisible; distributions; Lévy; processes; Stable; convergence; Triangular; arrays; Mixing; processes (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:115:y:2005:i:5:p:737-768 Ordering information: This journal article can be ordered from Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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