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On the exact order of normal approximation in multivariate renewal theory

Published online by Cambridge University Press:  14 July 2016

Ştefan P. Niculescu  and
Edward Omey
Ştefan P. Niculescu*
Affiliation:
Centre of Mathematical Statistics, Bucharest
Edward Omey*
Affiliation:
Economische Hogeschool Sint-Aloysius, Brussel
*
∗Postal address: Centre of Mathematical Statistics, 174 Ştirbei Vodǎ, 77104 Bucharest, Romania.
∗∗Postal address: Economisches Hogeschool Sint-Aloysius, 113 Broekstraat, 1000 Brussel, Belgium.
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Abstract

Equivalence of rates of convergence in the central limit theorem for the vector of maximum sums and the corresponding first-passage variables is established. A similar result for the vector of partial sums and the corresponding renewal variables is also given. The results extend to several dimensions the bivariate results of Ahmad (1981).

Keywords

RATES OF CONVERGENCECENTRAL LIMIT THEOREM
Type
Research Papers
Information
Journal of Applied Probability , Volume 22 , Issue 2 , June 1985 , pp. 280 - 287
Copyright
Copyright © Applied Probability Trust 1985 

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References

Ahmad, I. A. (1981) The exact order of normal approximation in bivariate renewal theory. Adv. Appl. Prob. 13, 113–128.Google Scholar
Bikjalis, A. (1971) On the central limit theorem in Rk. I. Litovsk. Mat. Sb. 11, 27–58.Google Scholar