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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Tauberian theorems for matrix regular variation


Authors: M. M. Meerschaert and H.-P. Scheffler
Journal: Trans. Amer. Math. Soc. 365 (2013), 2207-2221
MSC (2010): Primary 40E05; Secondary 44A10, 26A12
Published electronically: October 3, 2012
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Abstract: Karamata's Tauberian theorem relates the asymptotics of a nondecreasing right-continuous function to that of its Laplace-Stieltjes transform, using regular variation. This paper establishes the analogous Tauberian theorem for matrix-valued functions. Some applications to time series analysis are indicated.


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Additional Information

M. M. Meerschaert
Affiliation: Department of Statistics and Probability, Michigan State University, East Lansing, Michigan 48824
Email: mcubed@stt.msu.edu

H.-P. Scheffler
Affiliation: Fachbereich Mathematik, Universität Siegen, 57068 Siegen, Germany
Email: scheffler@mathematik.uni-siegen.de

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05751-5
PII: S 0002-9947(2012)05751-5
Received by editor(s): September 12, 2011
Published electronically: October 3, 2012
Additional Notes: Research of the first author was partially supported by NSF grants DMS-1025486, DMS-0803360, and NIH grant R01-EB012079.
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.