This article is cited in 9 papers

The matrix analogue of the Blackwell renewal theorem on the real line

M. S. Sgibnev

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: The full analogue of Blackwell's theorem is proved for a matrix renewal measure on the whole real line, both in the non-lattice and in the lattice cases. A complete result on a decomposition of Stone type for a matrix renewal measure is obtained. Asymptotic properties of solutions of systems of integral equations of renewal type on the real line are established.
Bibliography: 21 titles.

UDC: 517.962.28

MSC: Primary 60K05; Secondary 45M05

Received: 22.03.2005

DOI: 10.4213/sm1538

 English version: Sbornik: Mathematics, 2006, 197:3, 369–386

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