Topic
Renewal theory
About: Renewal theory is a research topic. Over the lifetime, 2381 publications have been published within this topic receiving 54908 citations.
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TL;DR: A generalized replacement model where a deteriorating system has two types of failures and is replaced at the Nth type I failure or first type II failure or at the working age T, whichever occurs first, is proposed.
61 citations
TL;DR: In this article, none-exponential asymptotics for solutions of two specific defective renewal equations are obtained, including the special cases of asymPTotics for a compound geometric distribution and the convolution of a compound geometrical distribution with a distribution function.
Abstract: Nonexponential asymptotics for solutions of two specific defective renewal equations are obtained. These include the special cases of asymptotics for a compound geometric distribution and the convolution of a compound geometric distribution with a distribution function. As applications of these results, we study the asymptotic behavior of the demographic birth rate of females, the perpetual put option in mathematics of finance, and the renewal function for terminating renewal processes.
61 citations
TL;DR: In this paper, a renewal risk model in which the surplus process of the insurance company is modelled by a compound fractional Poisson process is presented, and some results for the ruin probabilities are presented in various assumptions on the distribution of the claim sizes.
Abstract: We study a renewal risk model in which the surplus process of the insurance company is modelled by a compound fractional Poisson process. We establish the long-range dependence property of this non-stationary process. Some results for the ruin probabilities are presented in various assumptions on the distribution of the claim sizes.
60 citations
60 citations
TL;DR: In this article, the renewal process for the tails of random sums is studied and it is shown that for a class of sums, there is always a new worse than used (NWU) property.
Abstract: In this note, we derive an inequality for the renewal process. Then, using this inequality, together with an identity in terms of the renewal process for the tails of random sums, we prove that a class of random sums is always new worse than used (NWU). Thus, the well-known NWU property of geometric sums is extended to the class of random sums. This class is illustrated by some examples, including geometric sums, mixed geometric sums, certain mixed Poisson distributions and certain negative binomial sums.
60 citations