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December, 1973 Weak Convergence of Superpositions of Randomly Selected Partial Sums
Richard F. Serfozo
Ann. Probab. 1(6): 1044-1056 (December, 1973). DOI: 10.1214/aop/1176996810


The main results are functional central limit theorems for superpositions of randomly selected partial sums in which the random variables being summed are independent and have distributions in the domain of attraction of stable laws. These results extend those of Tucker and Sreehari concerning when convolutions of distributions are attracted to stable laws. Other functional central limit theorems are presented for more general sums. The results herein extend the central limit theory for additive processes on Markov chains.


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Richard F. Serfozo. "Weak Convergence of Superpositions of Randomly Selected Partial Sums." Ann. Probab. 1 (6) 1044 - 1056, December, 1973.


Published: December, 1973
First available in Project Euclid: 19 April 2007

zbMATH: 0271.60031
MathSciNet: MR365669
Digital Object Identifier: 10.1214/aop/1176996810

Primary: 60F05
Secondary: 60G50

Keywords: domain of attraction of stable law , functional central limit theorems , functionals of Markov processes , invariance principle , random environments , randomly selected partial sums , Stable processes , weak convergence

Rights: Copyright © 1973 Institute of Mathematical Statistics


Vol.1 • No. 6 • December, 1973
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