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April 2003 A characterization of $\boldsymbol{m}$-dependent stationary infinitely divisible sequences with applications to weak convergence
D. Harrelson, C. Houdré
Ann. Probab. 31(2): 849-881 (April 2003). DOI: 10.1214/aop/1048516538

Abstract

$m$-dependent stationary infinitely divisible sequences are characterized as a class of generalized finite moving average sequences via the structure of the associated Lévy measure. This characterization is used to find necessary and sufficient conditions for the weak convergence of centered and normalized partial sums of $m$-dependent stationary infinitely divisible sequences. Partial sum convergence for stationary infinitely divisible sequences that can be approximated by $m$-dependent ones is then studied.

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D. Harrelson. C. Houdré. "A characterization of $\boldsymbol{m}$-dependent stationary infinitely divisible sequences with applications to weak convergence." Ann. Probab. 31 (2) 849 - 881, April 2003. https://doi.org/10.1214/aop/1048516538

Information

Published: April 2003
First available in Project Euclid: 24 March 2003

zbMATH: 1058.60012
MathSciNet: MR1964951
Digital Object Identifier: 10.1214/aop/1048516538

Subjects:
Primary: 60E07 , 60F05 , 60G10

Keywords: $m$-dependence , Infinitely divisible , stable limit theorem , stationary

Rights: Copyright © 2003 Institute of Mathematical Statistics

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Vol.31 • No. 2 • April 2003
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