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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
Posted:
October 3, 2012
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References |
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Additional Information
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
Posted:
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.
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