The counting process and summation of a random number of random variables

Author:
O. V. Sugakova

Translated by:
V. Zayats

Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom **74** (2006).

Journal:
Theor. Probability and Math. Statist. **74** (2007), 181-189

MSC (2000):
Primary 60F05; Secondary 60K05

Published electronically:
July 9, 2007

MathSciNet review:
2336788

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The behavior of the tail of the sum of a random number of random variables is considered as . Estimates of the convergence of to the limit function are constructed in terms of renewal theory. The estimates are based on the variance of the counting process . A survey of bounds for is given for different sequences , in particular, for the case where the terms of the sequence are not identically distributed.

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Additional Information

**O. V. Sugakova**

Affiliation:
Department of Mathematics and Theoretical Radiophysics, Faculty of Radiophysics, Taras Shevchenko National University, Glushkov Avenue, 2, Building 5, Kyïv 03127, Ukraine

Email:
sugak@univ.kiev.ua

DOI:
http://dx.doi.org/10.1090/S0094-9000-07-00707-7

Keywords:
Nonhomogeneous renewal process,
counting process,
residual lifetime process,
variance of the counting process

Received by editor(s):
April 13, 2005

Published electronically:
July 9, 2007

Article copyright:
© Copyright 2007
American Mathematical Society