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), 181189
MSC (2000):
Primary 60F05; Secondary 60K05
Published electronically:
July 9, 2007
MathSciNet review:
2336788
Fulltext PDF Free Access
Abstract 
References 
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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/S0094900007007077
PII:
S 00949000(07)007077
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
