Invariance principles for renewal processes when only moments of low order exist

Starting from recent strong and weak approximations to the partial sums of i.i.d. random vectors (cf. U. Einmahl, Ann. Probab., 15 1419-1440), some corresponding invariance principles are developed for associated renewal processes and random sums. Optimality of the approximation is proved in the case when only two moments exist. Among other applications, a Darling-Erdös type extreme value theorem for renewal processes will be derived.

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Year of publication:	1988
Authors:	Steinebach, Josef
Published in:	Journal of Multivariate Analysis. - Elsevier, ISSN 0047-259X. - Vol. 26.1988, 2, p. 169-183
Publisher:	Elsevier
Keywords:	Invariance principles strong approximations weak approximations renewal processes random sums Wiener process extreme value theorem

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10005199402