Open Access
November, 1984 Strong Approximation of Extended Renewal Processes
Lajos Horvath
Ann. Probab. 12(4): 1149-1166 (November, 1984). DOI: 10.1214/aop/1176993145


We develop a strong approximation approach to extended multidimensional renewal theory. The consequences of this approximation are a Bahadur-Kiefer type representation of the renewal process in terms of partial sums, Strassen and Chung type laws of the iterated logarithm. We also give a characterization of the renewal process by four classes of deterministic curves in the sense of Revesz (1982). We generalize our results to the case of non-independent and/or nonidentically distributed random vectors.


Download Citation

Lajos Horvath. "Strong Approximation of Extended Renewal Processes." Ann. Probab. 12 (4) 1149 - 1166, November, 1984.


Published: November, 1984
First available in Project Euclid: 19 April 2007

zbMATH: 0552.60032
MathSciNet: MR757773
Digital Object Identifier: 10.1214/aop/1176993145

Primary: 60F17
Secondary: 60K05

Keywords: Laws of the iterated logarithm , Renewal process , strong approximation , Wiener process

Rights: Copyright © 1984 Institute of Mathematical Statistics

Vol.12 • No. 4 • November, 1984
Back to Top