J Austral Math Soc Ser A 45 pp381--388, 1988.

Rates of Convergence for Renewal Sequences in the Null-Recurrent Case

Richard Isaac

Abstract

Motivated by work of Garsia and Lamperti we consider null-recurrent renewal sequences with a regularly varying tail and seek information about their rate of convergence to zero. The main result shows us that such sequences subject to a monotonicity condition obey a limit law whatever the value of the exponent a is, 0 < a < 1. This monotonicity property is seen to hold for a large class of renewal sequences, and therefore includes the sequences generated by reversible Markov chains. Several subsidiary results are proved.

1980 AMS Subject Classification (1985 Revision): primary 60K05; secondary 60J10

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Authors

Richard Isaac

Department of Mathematics and Computer Science, Lehman College, CUNY, Bronx, New York 10468, U.S.A.