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On the asymptotic distribution of multivariate renewal processes

Published online by Cambridge University Press:  14 July 2016

Ştefan P. Niculescu
Ştefan P. Niculescu*
Affiliation:
Centre of Mathematical Statistics, Bucharest
*
∗Postal address: Centre of Mathematical Statistics, 174 Ştirbei Vodă, 77104 Bucharest, Romania.
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Abstract

Using a result of Bikjalis (1971) concerning the rate of convergence in the multidimensional central limit theorem we obtain informations about some limit distributions in multivariate renewal theory.

Keywords

MULTIVARIATE RENEWAL THEORYCENTRAL LIMIT THEOREMRATES OF CONVERGENCE
Type
Short Communications
Information
Journal of Applied Probability , Volume 21 , Issue 3 , September 1984 , pp. 639 - 645
Copyright
Copyright © Applied Probability Trust 1984 

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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. (in Russian) Litovsk. Mat. Sb. 11, 27–58.Google Scholar
Billingsley, P. (1968) Convergence of Probability Measures. Wiley, New York.Google Scholar
Csenki, A. (1979) An invariance principle in k-dimensional extended renewal theory. J. Appl. Prob. 16, 567–574.Google Scholar
Hunter, J. J. (1974) Renewal theory in two dimensions: asymptotic results. Adv. Appl. Prob. 6, 546–562.Google Scholar