Tauberian theorems for matrix regular variation

Meerschaert, M.; Scheffler, H.-P.

doi:10.1090/S0002-9947-2012-05751-5

Tauberian theorems for matrix regular variation
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by M. M. Meerschaert and H.-P. Scheffler PDF

Trans. Amer. Math. Soc. 365 (2013), 2207-2221 Request permission

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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