A renewal theorem in the finite-mean case期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

A renewal theorem in the finite-mean case

Authors:	J L Geluk

Institution:	Econometric Institute, Erasmus University Rotterdam, P.O. Box 1738, NL-3000 DR Rotterdam, The Netherlands

Abstract:	Let be a c.d.f. on $(0,\infty )$ such that $\overline F(.) \equiv 1-F(.)$ is regularly varying with exponent $-\alpha ,~1<\alpha <2$ . Then $U(t)- \frac {t}{\mu } -\frac {1}{\mu ^2} \int _0^t \int _s^\infty \overline F(v) dv ds = O(t^4 \overline F(t)^2 \overline F(t^2\overline F(t)))$ as $t \to \infty$ , where is the renewal function associated with . Moreover similar estimates are given for distributions in the domain of attraction of the normal distribution and for the variance of The estimates improve earlier results of Teugels and Mohan.

Keywords:	Renewal function regular variation key renewal theorem domain of attraction

	点击此处可从《Proceedings of the American Mathematical Society》浏览原始摘要信息
	点击此处可从《Proceedings of the American Mathematical Society》下载免费的PDF全文