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

DOI:
https://doi.org/10.1090/S0002-9947-2012-05751-5

Published electronically:
October 3, 2012

MathSciNet review:
3009656

Full-text PDF

Abstract | References | Similar Articles | 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:
https://doi.org/10.1090/S0002-9947-2012-05751-5

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.