caa a22 4500 386307857 CHVBK 20180307111535.0 cr unu---uuuuu 161130e198812 xx s 000 0 eng 10.1017/S1446788700031098 doi S1446788700031098 pii (NATIONALLICENCE)cambridge-10.1017/S1446788700031098 Isaac Richard Department of Mathematics and Computer Science, Lehman College, CUNY Bronx, New York 10468, U.S.A. Rates of convergence for renewal sequences in the null-recurrent case [Elektronische Daten] [Richard Isaac] 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 that such sequences subject to a monotonicity condition obey a limit law whatever the value of the exponent α is, 0 < α < 1. This monotonicity property is seen to hold for a large class of renewal sequences, the so-called Kaluza sequences. This class includes moment sequences, and therefore includes the sequences generated by reversible Markov chains. Several subsidiary results are proved. Copyright © Australian Mathematical Society 1988 primary 60 K 05 nationallicence secondary 60 J 10 nationallicence Journal of the Australian Mathematical Society Cambridge University Press 45/3(1988-12), 381-388 1446-7887 45:3<381 1988 45 JAZ https://doi.org/10.1017/S1446788700031098 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S1446788700031098 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Isaac Richard Department of Mathematics and Computer Science, Lehman College, CUNY Bronx, New York 10468, U.S.A NATIONALLICENCE 773 0- Journal of the Australian Mathematical Society Cambridge University Press 45/3(1988-12), 381-388 1446-7887 45:3<381 1988 45 JAZ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge