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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: In this paper, an approach that more explicitly uses a Markov renewal theoretic framework and thus leads to a simplified derivation of their main results together with a number of new ones is presented.
20 citations
20 citations
TL;DR: In this paper, a semi-Markovian random walk with two reflecting barriers is constructed mathematically and non-stationary distribution functions of it are expressed by means of the probability characteristics of renewal process {T n } and random walk {Y n } without barriers.
Abstract: In this paper, the semi-Markovian random walk with two reflecting barriers is constructed mathematically and non-stationary distribution functions of it are expressed by means of the probability characteristics of renewal process {T n } and random walk {Y n } without barriers. In particular, when the time between two jump instants has exponential or Erlang distribution, explicit formulae are obtained for non-stationary distribution functions of the process. Moreover, explicit expressions are given for expected value, variance and moment generating function of the first reflection moment, an important boundary functional, of the process from lower reflecting barrier.
20 citations
TL;DR: In this paper, an estimator based on the number of renewals Nt in a fixed time t is proposed to estimate the parameter k in a renewal process where the interarrival times have gamma(μ, k) distribution.
20 citations
TL;DR: The first two moments and covariance of the aggregate discounted claims have been found for a stochastic interest rate, from which the inflation rate has been subtracted, and for a claims number process that is an ordinary or a delayed renewal process.
Abstract: The first two moments and the covariance of the aggregate discounted claims have been found for a stochastic interest rate, from which the inflation rate has been subtracted, and for a claims number process that is an ordinary or a delayed renewal process. Hereafter we extend the preceding results by presenting recursive formulas for the joint moments of this risk process, for a constant interest rate, and non-recursive formulas for higher joint moments when the interest rate is stochastic. Examples are given for exponential claims inter-arrival times and for the Ho-Lee-Merton interest rate model.
19 citations