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: In this paper, some basic concepts from the theory of point processes are recalled and expanded, and some notions of stochastic comparisons, which compare whole processes, are introduced, illustrated by stochastically comparing renewal and related processes.
Abstract: First, some basic concepts from the theory of point processes are recalled and expanded. Then some notions of stochastic comparisons, which compare whole processes, are introduced. The use of these notions is illustrated by stochastically comparing renewal and related processes. Finally, applications of the different notions of stochastic ordering of point processes to many replacement policies are given.
15 citations
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01 Jan 1974TL;DR: In a pure loss GI/G/ 1 queueing system, necessary and sufficient conditions are given for the output to be a renewal process.
Abstract: In a pure loss GI/G/ 1 queueing system, necessary and sufficient conditions are given for the output to be a renewal process. These conditions involve dependence between the service distribution and the renewal function of the arrival process: for example, if pr {service time 0, then it is sufficient for the renewal function to be that of a quasi-Poisson process with index ξ.
15 citations
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TL;DR: In this paper, the authors present a standard procedure for the simulation of risk processes for insurance companies, which is vital for the calculation of the amount of loss that may occur, and also appears naturally in rating triggered step-up bonds.
Abstract: The simulation of risk processes is a standard procedure for insurance companies. The generation of simulated (aggregated) claims is vital for the calculation of the amount of loss that may occur. Simulation of risk processes also appears naturally in rating triggered step-up bonds, where the interest rate is bound to random changes of the companies? ratings.
15 citations
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TL;DR: In this paper, a strong stationary dual chain X* whose first hitting times give sharp bounds on the convergence to stationarity for X was constructed, and the first extension of the stopping time arguments of Aldous and Diaconis to infinite state spaces.
Abstract: Let X1,X2,… be an ergodic Markov chain on the countable state space. We construct a strong stationary dual chain X* whose first hitting times give sharp bounds on the convergence to stationarity for X. Examples include birth and death chains, queueing models, and the excess life process of renewal theory. This paper gives the first extension of the stopping time arguments of Aldous and Diaconis [1,2] to infinite state spaces.
15 citations
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TL;DR: In this paper, the class of inverses of a p-thinned renewal process is considered, and it is shown that this class consists of Cox and renewal processes if and only if the given thinned process is Cox and renewing.
Abstract: The class of inverses of a p-thinned renewal process is considered. It is shown that this class consists of renewal processes. It consists of Cox and renewal processes if and only if the given thinned process is Cox and renewal. In the non-Cox case, there exists a unique top renewal process, which by thinning generates all the possible inverses. Conditions for a renewal process to be a top process are given. Finally, a gamma renewal process is shown to be a top process when a > 1, where a is the shape parameter of the gamma distribution. POINT PROCESS; THINNED POINT PROCESS; INVERSE THINNING; COX PROCESS; GAMMA RENEWAL PROCESS
15 citations