A characterization of m-dependent stationary infinitely divisible sequences with applications to weak convergence
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D. Harrelson [1] ; C. Houdré [2]
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[1] Hope College
Hope College
City of Holland, Estados Unidos
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[2] Georgia Institute of Technology
Georgia Institute of Technology
Estados Unidos
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- Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 31, Nº. 2, 2003, págs. 849-881
- Idioma: inglés
- DOI: 10.1214/aop/1048516538
- Texto completo no disponible (Saber más ...)
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Resumen
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.
