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, the joint distribution of first passage time τ, pre-exit time τρ, and τρ−1 (i.e., the instant one phase prior to the first passage) in a multivariate quasi Poisson process is derived in a closed form.
Abstract: We introduce and analyze a delayed renewal process = {τ0,τ1,…} marked by a multivariate random walk (,) and its behavior about fixed levels to be crossed by one of the components of (,). We derive the joint distribution of first passage time τρ, pre-exit time τρ−1 (i.e., the instant one phase prior to the first passage time), and the respective values of (,) at τρ and τρ−1 in a closed form. The results obtained are then applied to a multivariate quasi Poisson process Π, forming a random walk ((Π),) embedded in Π over . Processes like these can model various phenomena including stock market and option trading. One of the central issues in the investigation of ((Π),) is to obtain the information about Π at any moment of time in random vicinities of τρ and τρ−1 previously available only upon . The results offer, again, closed form functionals. Numerous examples throughout the paper illustrate introduced constructions and connect the results with real-world applications, most prominentl...
14 citations
TL;DR: In this paper, the output is interpreted by random demand and the input by a deterministic production plus random returns, and two control policies are considered: continuous review and periodic review.
Abstract: We present the production version of two EOQ-type models in heavy traffic. The output is interpreted by random demand and the input by a deterministic production plus random returns. In the ON part of the cycle, the inventory content is a reflected Brownian motion, and in the OFF part, it is a Brownian motion with a negative drift. The ON/OFF periods generate an alternative renewal process and the content-level process is a regenerative process. Two control policies are considered. In one policy that is natural under conditions of continuous review, production is stopped when the content level in the ON period reaches a predetermined level q. In the other policy, which resembles periodic review, production is stopped when the ON time reaches a predetermined time t0.
13 citations
TL;DR: In this article, an intermittent two-state noise can be modelled through a renewal process characterized by two different time scales, and the equivalence between the renewal approach and the enlarged master equation is shown.
Abstract: An intermittent two-state noise can be modelled through a renewal process characterized by two different time scales. A (four state) Markovian embedding of this non-Markovian process is presented. The equivalence between the renewal approach and the enlarged master equation is shown. Analytical results for n-time moments of the intermittent dichotomic noise are obtained. The Monte Carlo simulations supports our analytical results. The advantage of using the enlarged master equation for calculating higher order moments is established.
13 citations
TL;DR: An original algorithm is developed to estimate the conditional intensity function by preserving its structure in terms of the trend function and the underlying renewal process by using kernel smoothing techniques.
13 citations
TL;DR: In this article, a generalized discounted penalty function is studied by using random walk techniques and the renewal theory, where the downward jumps represent the claims as usual and the upward jumps are also allowed to explain random gains.
13 citations