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

Josef Steinebach

Journal of Multivariate Analysis, 1988, vol. 26, issue 2, 169-183

Abstract: 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.

Keywords: Invariance; principles; strong; approximations; weak; approximations; renewal; processes; random; sums; Wiener; process; extreme; value; theorem (search for similar items in EconPapers)
Date: 1988
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