scispace - formally typeset
Search or ask a question
Topic

Renewal theory

About: Renewal theory is a research topic. Over the lifetime, 2381 publications have been published within this topic receiving 54908 citations.


Papers
More filters
Journal ArticleDOI
TL;DR: In this article, it was shown that if a stochastic process whose finite-dimensional, conditional distributions are asymptotically close to those of a Markov random walk satisfying the conditions of Kesten's Markov renewal theorem has the same limiting distribution as that of the overshoot of a perturbed Markov Random Walk, then the slow change condition on the perturbation process can be strengthened.

9 citations

Journal ArticleDOI
Dug Hun Hong1
TL;DR: This note proves the same results without the assumption of continuity of the inter-arrival times and rewards of the fuzzy renewal rewards theorem.
Abstract: Recently, Zhao and Liu [IJUFKS 11 (2003) 573–586] proposed a "fuzzy elementary renewal theorem" and "fuzzy renewal rewards theorem" for a renewal process in which the inter-arrival times and rewards are characterized as continuous fuzzy variables. The continuity assumption is restrictive. In this note, we prove the same results without the assumption of continuity of the inter-arrival times and rewards.

9 citations

Journal ArticleDOI
TL;DR: This work analyses such a stochastic process when the interarrival times separating consecutive velocity changes (and jumps) have generalized Mittag-Leffler distributions, and constitute the random times of a fractional alternating Poisson process.
Abstract: The basic jump-telegraph process with exponentially distributed interarrival times deserves interest in various applied fields such as financial modelling and queueing theory. Aiming to propose a more general setting, we analyse such a stochastic process when the interarrival times separating consecutive velocity changes (and jumps) have generalized Mittag-Leffler distributions, and constitute the random times of a fractional alternating Poisson process. By means of renewal theory-based issues we obtain the forward and backward transition densities of the motion in series form, and prove their uniform convergence. Specific attention is then given to the case of jumps with constant size, for which we also obtain the mean of the process. Finally, we investigate the first-passage time of the process through a constant positive boundary, providing its formal distribution and suitable lower bounds.

9 citations

Journal ArticleDOI
TL;DR: The main results show that the proposed mathematical models result in power law distribution under quite general polynomial Gartner-Ellis conditions, the generality of which could explain the ubiquitous nature of power law distributions.
Abstract: Power law distributions have been repeatedly observed in a wide variety of socioeconomic, biological, and technological areas. In many of the observations, e.g., city populations and sizes of living organisms, the objects of interest evolve because of the replication of their many independent components, e.g., births and deaths of individuals and replications of cells. Furthermore, the rates of replications are often controlled by exogenous parameters causing periods of expansion and contraction, e.g., baby booms and busts, economic booms and recessions, etc. In addition, the sizes of these objects often have reflective lower boundaries, e.g., cities do not fall below a certain size, low-income individuals are subsidized by the government, companies are protected by bankruptcy laws, etc. Hence, it is natural to propose reflected modulated branching processes as generic models for many of the preceding observations. Indeed, our main results show that the proposed mathematical models result in power law distributions under quite general polynomial Gartner-Ellis conditions, the generality of which could explain the ubiquitous nature of power law distributions. In addition, on a logarithmic scale, we establish an asymptotic equivalence between the reflected branching processes and the corresponding multiplicative ones. The latter, as recognized by Goldie [Goldie, C. M. 1991. Implicit renewal theory and tails of solutions of random equations. Ann. Appl. Probab.1(1) 126--166], is known to be dual to queueing/additive processes. We emphasize this duality further in the generality of stationary and ergodic processes.

9 citations

Journal ArticleDOI
TL;DR: This work presents a complete analysis of the free energy singularities, which include the localization-delocalization critical point and (in general) other critical points that have been only partially captured in the physical literature.

9 citations


Network Information
Related Topics (5)
Markov chain
51.9K papers, 1.3M citations
92% related
Stochastic process
31.2K papers, 898.7K citations
88% related
Probability distribution
40.9K papers, 1.1M citations
84% related
Estimator
97.3K papers, 2.6M citations
81% related
Upper and lower bounds
56.9K papers, 1.1M citations
79% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202327
202260
202173
202083
201973
201886