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Methodology and Computing in Applied Probability最新文献

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Two-sided Bounds for some Quantities in the Delayed Renewal Process 延迟更新过程中某些量的双侧界限
IF 0.9 4区 数学
Methodology and Computing in Applied Probability Pub Date : 2024-08-02 DOI: 10.1007/s11009-024-10088-9
Stathis Chadjiconstantinidis
{"title":"Two-sided Bounds for some Quantities in the Delayed Renewal Process","authors":"Stathis Chadjiconstantinidis","doi":"10.1007/s11009-024-10088-9","DOIUrl":"https://doi.org/10.1007/s11009-024-10088-9","url":null,"abstract":"<p>In this paper we obtain some “general” two-sided bounds for the delayed renewal function, in the sense that the bounds are valid for any arbitrary distributions of the inter-arrival times. Also, we give a sequence of monotone non-decreasing (non-increasing) lower (upper) general bounds converging to the delayed renewal function. By considering several aging or reliability classes for the distribution of the interarrival times (e.g., <span>(DFR)</span>, bounded mean residual lifetime, <span>(NBUE)</span>, <span>(NWUE)</span>, bounded failure rate, <span>(DMRL)</span>, <span>(IMRL)</span>) we give upper and lower bounds for the delayed renewal function, and moreover by assuming the usual stochastic order between the first and the subsequent interarrival times, we give sequences of monotone non-decreasing (non-increasing) lower (upper) bounds converging to the delayed renewal function. Also, some sequences of bounds for the delayed renewal function in terms of the ordinary renewal function are given. Sequences of monotone non-decreasing (non-increasing) lower (upper) bounds for the delayed renewal density are also given. Finally, we obtain upper and lower bounds for the expected number of renewals over a finite interval, and as a result, we get an improvement of the upper bounds obtained by Lorden (Ann Math Statist 41:520–527, 1970) and Losidis and Politis (2022) for the expected number of renewals over a finite interval under the ordinary renewal process.</p>","PeriodicalId":18442,"journal":{"name":"Methodology and Computing in Applied Probability","volume":"70 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141886954","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Dynamics of a Stochastic Regime-Switching Four-Species Food Chain Model with Distributed Delays and Harvesting 带有分布式延迟和收获的随机制度转换四物种食物链模型的动态变化
IF 0.9 4区 数学
Methodology and Computing in Applied Probability Pub Date : 2024-07-17 DOI: 10.1007/s11009-024-10095-w
Sheng Wang, Lijuan Dong
{"title":"Dynamics of a Stochastic Regime-Switching Four-Species Food Chain Model with Distributed Delays and Harvesting","authors":"Sheng Wang, Lijuan Dong","doi":"10.1007/s11009-024-10095-w","DOIUrl":"https://doi.org/10.1007/s11009-024-10095-w","url":null,"abstract":"<p>This paper concerns the dynamics of a stochastic regime-switching four-species food chain model with distributed delays, Lévy jumps and harvesting in a polluted environment. First, under some basic assumptions, criterions about stochastic persistence and extinction of each species are established. Then, sufficient and necessary conditions for the existence of optimal harvesting policy (OHP) are obtained, as well as the expressions for the optimal harvesting effort (OHE) and the maximum of expectation of sustainable yield (MESY). The effects of both environmental noises and delays on the stochastic persistence, extinction and OHP of the model are revealed. Some results on food chain models without telephone noises or distributed delays are extended and improved.</p>","PeriodicalId":18442,"journal":{"name":"Methodology and Computing in Applied Probability","volume":"63 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141721384","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Asymptotic Behaviors of the VaR and CVaR Estimates for Widely Orthant Dependent Sequences 宽正交依赖序列的 VaR 和 CVaR 估计值的渐近行为
IF 0.9 4区 数学
Methodology and Computing in Applied Probability Pub Date : 2024-07-06 DOI: 10.1007/s11009-024-10093-y
Li Yongming, Li Naiyi, Luo Zhongde, Xing Guodong
{"title":"Asymptotic Behaviors of the VaR and CVaR Estimates for Widely Orthant Dependent Sequences","authors":"Li Yongming, Li Naiyi, Luo Zhongde, Xing Guodong","doi":"10.1007/s11009-024-10093-y","DOIUrl":"https://doi.org/10.1007/s11009-024-10093-y","url":null,"abstract":"<p>This paper considers some asymptotics of value-at-risk (VaR) and conditional value-at-risk (CVaR) estimates in the cases of extended negatively dependent (END) and widely orthant dependent (WOD) sequences. The Bahadur representation and strong consistency of VaR estimator are obtained, and the strong convergence rate of CVaR estimator is obtained based on END and WOD sequences. In addition, the asymptotic normality of VaR estimator is given based on END sequence. Finally, some simulations to study the numerical performance of the consistency for VaR and CVaR estimators are given in the case of WOD sample. Our results extend and improve some corresponding results.</p>","PeriodicalId":18442,"journal":{"name":"Methodology and Computing in Applied Probability","volume":"24 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141576340","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Transient Analysis of a Modified Differentiated Vacation Queueing System for Energy-Saving in WiMAX 用于 WiMAX 节能的改进型差异化休假排队系统的瞬态分析
IF 0.9 4区 数学
Methodology and Computing in Applied Probability Pub Date : 2024-07-04 DOI: 10.1007/s11009-024-10094-x
A. Mohammed Shapique, R. Sudhesh, S. Dharmaraja
{"title":"Transient Analysis of a Modified Differentiated Vacation Queueing System for Energy-Saving in WiMAX","authors":"A. Mohammed Shapique, R. Sudhesh, S. Dharmaraja","doi":"10.1007/s11009-024-10094-x","DOIUrl":"https://doi.org/10.1007/s11009-024-10094-x","url":null,"abstract":"<p>A modified differentiated vacation queueing system with a close-down period and impatient customers is investigated in this research paper. The proposed model can be applied to study the energy management mechanisms of WiMAX and tethered high altitude platform (HAP) systems. In this system, the WiMAX mobile station (MS) switches to a close-down period for a random duration at the end of the busy period. At the end of the close-down period, if the system is non-empty, the MS switches to a functional state. Otherwise, the MS takes an ordinary vacation. The MS switches to a working vacation (WV) if the system is empty at the end of the ordinary vacation period. Jobs arriving during the WV are served at a slower service rate. Jobs may become impatient in any state of the system except during the regular busy period. Explicit expressions for the transient and steady-state probabilities of this system are obtained using continued fraction and confluent hypergeometric functions. Furthermore, performance indices such as mean, variance, average abandonment rate, and system throughput are computed. Finally, a cost-profit analysis and graphical illustrations are provided.</p>","PeriodicalId":18442,"journal":{"name":"Methodology and Computing in Applied Probability","volume":"42 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141550356","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Note on the Distribution of the Extreme Degrees of a Random Graph via the Stein-Chen Method 通过 Stein-Chen 方法研究随机图极值度分布的说明
IF 0.9 4区 数学
Methodology and Computing in Applied Probability Pub Date : 2024-07-02 DOI: 10.1007/s11009-024-10091-0
Yaakov Malinovsky
{"title":"A Note on the Distribution of the Extreme Degrees of a Random Graph via the Stein-Chen Method","authors":"Yaakov Malinovsky","doi":"10.1007/s11009-024-10091-0","DOIUrl":"https://doi.org/10.1007/s11009-024-10091-0","url":null,"abstract":"<p>We offer an alternative proof, using the Stein-Chen method, of Bollobás’ theorem concerning the distribution of the extreme degrees of a random graph. Our proof also provides a rate of convergence of the extreme degree to its asymptotic distribution. The same method also applies in a more general setting where the probability of every pair of vertices being connected by edges depends on the number of vertices.</p>","PeriodicalId":18442,"journal":{"name":"Methodology and Computing in Applied Probability","volume":"78 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141501218","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Analysis of Renewal Batch Arrival Queues with Multiple Vacations and Geometric Abandonment 具有多次空闲和几何放弃的更新批次到达队列分析
IF 0.9 4区 数学
Methodology and Computing in Applied Probability Pub Date : 2024-06-03 DOI: 10.1007/s11009-024-10089-8
Veena Goswami, Gopinath Panda
{"title":"Analysis of Renewal Batch Arrival Queues with Multiple Vacations and Geometric Abandonment","authors":"Veena Goswami, Gopinath Panda","doi":"10.1007/s11009-024-10089-8","DOIUrl":"https://doi.org/10.1007/s11009-024-10089-8","url":null,"abstract":"<p>We investigate the dynamics of customer geometric abandonment within a queueing framework characterized by renewal input batch arrivals and multiple vacations. Customers’ impatience becomes evident when confronted with server vacations, triggering instances of abandonment. This phenomenon reduces the number of customers within the system during abandonment epochs following a geometric distribution. The probability of customers leaving the queue escalates with prolonged waiting times. We derive concise and closed-form expressions for system-length distributions at pre-arrival and arbitrary epochs by harnessing the power of supplementary variable and difference operator methods. Furthermore, we elucidate specific instances of our model, shedding light on its versatility. To substantiate our theoretical framework, we provide a series of illustrative numerical experiments presented through meticulously crafted tables and graphs, thereby showcasing the robustness and applicability of our methodology.</p>","PeriodicalId":18442,"journal":{"name":"Methodology and Computing in Applied Probability","volume":"4 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141252993","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Collocation Method for Nonlinear Stochastic Differential Equations Driven by Fractional Brownian Motion and its Application to Mathematical Finance 分数布朗运动驱动的非线性随机微分方程的配位法及其在数学金融中的应用
IF 0.9 4区 数学
Methodology and Computing in Applied Probability Pub Date : 2024-05-13 DOI: 10.1007/s11009-024-10087-w
P. K. Singh, S. Saha Ray
{"title":"A Collocation Method for Nonlinear Stochastic Differential Equations Driven by Fractional Brownian Motion and its Application to Mathematical Finance","authors":"P. K. Singh, S. Saha Ray","doi":"10.1007/s11009-024-10087-w","DOIUrl":"https://doi.org/10.1007/s11009-024-10087-w","url":null,"abstract":"<p>The main aim of this article is to demonstrate the collocation method based on the barycentric rational interpolation function to solve nonlinear stochastic differential equations driven by fractional Brownian motion. First of all, the corresponding integral form of the nonlinear stochastic differential equations driven by fractional Brownian motion is introduced. Then, collocation points followed by the Gauss-quadrature formula and Simpson’s quadrature method are used to reduce them into a system of algebraic equations. Finally, the approximate solution is obtained using Newton’s method. The rigorous convergence and error analysis of the presented method has been discussed in detail. The proposed method has been applied to some well-known stochastic models, such as the stock model and a few other examples, to demonstrate the applicability and plausibility of the discussed method. Also, the numerical results of the collocation method based on the barycentric rational interpolation function and barycentric Lagrange interpolation function get compared with an exact solution.</p>","PeriodicalId":18442,"journal":{"name":"Methodology and Computing in Applied Probability","volume":"103 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140932644","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Two-sided Bounds for Renewal Equations and Ruin Quantities 更新方程和废墟量的双侧界限
IF 0.9 4区 数学
Methodology and Computing in Applied Probability Pub Date : 2024-05-08 DOI: 10.1007/s11009-024-10075-0
Stathis Chadjiconsatntinidis
{"title":"Two-sided Bounds for Renewal Equations and Ruin Quantities","authors":"Stathis Chadjiconsatntinidis","doi":"10.1007/s11009-024-10075-0","DOIUrl":"https://doi.org/10.1007/s11009-024-10075-0","url":null,"abstract":"<p>In this paper, the objective is to provide sequences of improved non-increasing (non-decreasing) upper (lower) bounds for the solution of (defective) renewal equations in terms of the right-tail probability of a compound geometric distribution. Exponential (Lundberg type) and non-exponential type bounds are also derived. Also, under several reliability classifications, some new as well as improvements of well-known bounds are given. The results are then applied to obtain refinements of the bounds for several ruin related quantities, (such as the deficit at ruin, the joint distribution of the surplus prior to and at ruin, the mean deficit at ruin and the stop-loss premium, and the compound geometric densities). Bounds for the renewal function are also given.</p>","PeriodicalId":18442,"journal":{"name":"Methodology and Computing in Applied Probability","volume":"66 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140932570","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Bahadur Representation for Empirical and Smooth Quantile Estimators Under Association 关联条件下经验和平滑量子估计器的巴哈杜尔表示法
IF 0.9 4区 数学
Methodology and Computing in Applied Probability Pub Date : 2024-05-01 DOI: 10.1007/s11009-024-10086-x
Nour-Eddine Berrahou, Salim Bouzebda, Lahcen Douge
{"title":"The Bahadur Representation for Empirical and Smooth Quantile Estimators Under Association","authors":"Nour-Eddine Berrahou, Salim Bouzebda, Lahcen Douge","doi":"10.1007/s11009-024-10086-x","DOIUrl":"https://doi.org/10.1007/s11009-024-10086-x","url":null,"abstract":"<p>In this paper, the Bahadur representation of the empirical and Bernstein polynomials estimators of the quantile function based on associated sequences are investigated. The rate of approximation depends on the rate of decay in covariances, and it converges to the optimal rate observed under independence when the covariances quickly approach zero. As an application, we establish a Berry-Esseen bound with the rate <span>(O(n^{-1/3}))</span> assuming polynomial decay of covariances. All these results are established under fairly general conditions on the underlying distributions. Additionally, we perform Monte Carlo simulations to evaluate the finite sample performance of the suggested estimators, utilizing an associated and non-mixing model.</p>","PeriodicalId":18442,"journal":{"name":"Methodology and Computing in Applied Probability","volume":"11 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140835335","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Cyclic Random Motion in $$mathbb {R}^3$$ Driven by Geometric Counting Processes 几何计数过程驱动的 $$mathbb {R}^3$$ 循环随机运动
IF 0.9 4区 数学
Methodology and Computing in Applied Probability Pub Date : 2024-04-16 DOI: 10.1007/s11009-024-10083-0
Antonella Iuliano, Gabriella Verasani
{"title":"A Cyclic Random Motion in $$mathbb {R}^3$$ Driven by Geometric Counting Processes","authors":"Antonella Iuliano, Gabriella Verasani","doi":"10.1007/s11009-024-10083-0","DOIUrl":"https://doi.org/10.1007/s11009-024-10083-0","url":null,"abstract":"<p>We consider the random motion of a particle that moves with constant velocity in <span>(mathbb {R}^3)</span>. The particle can move along four different directions that are attained cyclically. It follows that the support of the stochastic process describing the particle’s position at a fixed time is a tetrahedron. We assume that the sequence of sojourn times along each direction follows a Geometric Counting Process (GCP). When the initial condition is fixed, we obtain the explicit form of the probability law of the process, for the particle’s position. We also investigate the limiting behavior of the related probability density when the intensities of the four GCPs tend to infinity. Furthermore, we show that the process does not admit a stationary density. Finally, we introduce the first-passage-time problem for the first component of the process through a constant positive boundary providing the bases for future developments.</p>","PeriodicalId":18442,"journal":{"name":"Methodology and Computing in Applied Probability","volume":"19 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140614062","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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