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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: The Gerber–Shiu discounted penalty function in the delayed renewal model is expressed in terms of the corresponding Gerber-Shiu function inThe ordinary renewal model as a discrete analogy of the classical Sparre–Anderson risk model.
24 citations
TL;DR: In this paper, a number of weak asymptotics are established for certain maximum increments of renewal counting processes via strong invariance, and the results are suggested to serve as a testing device for detecting changes in the intensity of the underlying renewal process.
24 citations
TL;DR: This work uses renewal theory to obtain some asymptotic properties of finite-state noiseless channels and provides the asymPTotic performance of two of the Perl, Garey and Even (1975) prefix condition codes.
Abstract: Renewal theory is a powerful tool in the analysis of source codes. We use renewal theory to obtain some asymptotic properties of finite-state noiseless channels. We discuss the relationship between these results and earlier uses of renewal theory to analyze the Lempel-Ziv (1977, 1978) codes and the Tunstall (1967) code. As a new application of our results, we provide the asymptotic performance of two of the Perl, Garey and Even (1975) prefix condition codes.
24 citations
TL;DR: In this article, the authors give necessary and sufficient conditions for finiteness of moments of passage times of general Levy processes above horizontal, linear or certain curved boundaries, leading to estimates of the rate of growth of certain expectations, constituting generalised kinds of renewal theorems.
Abstract: We give necessary and sufficient conditions, in terms of characteristics of the process, for finiteness of moments of passage times of general Levy processes above horizontal, linear or certain curved boundaries. They apply in particular to processes which drift almost surely to infinity, and lead to estimates of the rate of growth of certain expectations, constituting generalised kinds of renewal theorems. Further results concern the inverse local time at the maximum and the ladder height process, the amount of time spent below a given level, and the overall minimum of the Levy process.
24 citations
TL;DR: In this article, a defective renewal equation for the conditional Gerber-Shiu expected discounted penalty function is obtained based on the associated ordinary renewal process, and the relationship between the conditional expected discount function in the ordinary renewal case and that in the delayed renewal case is established.
Abstract: This paper considers the compound Markov binomial risk model proposed by Cossette et al. (2003 2004). Two discrete-time renewal (ordinary renewal and delayed renewal) risk processes associated with the compound Markov binomial risk model are analyzed. Based on the associated ordinary renewal process, a defective renewal equation for the conditional Gerber–Shiu expected discounted penalty function is obtained. The relationship between the conditional expected discounted penalty function in the ordinary renewal case and that in the delayed renewal case is then established. From these results, the conditional ultimate probability of ruin as well as the conditional joint distribution of the surplus just prior to ruin and the deficit at ruin are studied. Finally, it is shown that a modified version of the compound Markov binomial risk model is a special case of the discrete-time semi-Markov risk model introduced by Reinhard and Snoussi (2001 2002).
23 citations