A minimal uniform renewal theorem and transition phenomena for a nonhomogeneous perturbation of the renewal equation
Author:M. V. Kartashov Translated by:S. Kvasko Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom 82 (2010).
Journal:
Theor. Probability and Math. Statist. 82 (2011), 27-41
MSC (2010):
Primary 60J45; Secondary 60A05, 60K05
Published electronically:
August 2, 2011
MathSciNet review:2790481 Full-text PDF
Abstract: We consider the classical continuous time nonhomogeneous renewal equation on the half-line, that is, the integral Volterra equation with a nonnegative bounded kernel. It is assumed that the kernel can be approximated by a convolution kernel generated by a strong substochastic distribution in the large time scale. We study the scheme of series (transition phenomena) where the corresponding defect tends to zero and the time scale tends to infinity. We find the limit of a solution of the renewal equation under certain assumptions. This result is based on a minimal renewal theorem in the scheme of series.
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M. V. Kartashov Affiliation:
Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 2, Kiev 03127, Ukraine
Email:
nkartashov@skif.com.ua