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Inequalities between time and customer averages for HNB(W)UE arrival processes HNB(W)UE 到达过程的时间和客户平均值之间的不等式
IF 1 4区 数学
Journal of Applied Probability Pub Date : 2024-03-21 DOI: 10.1017/jpr.2023.120
Shigeo Shioda, Kana Nakano
{"title":"Inequalities between time and customer averages for HNB(W)UE arrival processes","authors":"Shigeo Shioda, Kana Nakano","doi":"10.1017/jpr.2023.120","DOIUrl":"https://doi.org/10.1017/jpr.2023.120","url":null,"abstract":"We show that for arrival processes, the ‘harmonic new better than used in expectation’ (HNBUE) (or ‘harmonic new worse than used in expectation’, HNWUE) property is a sufficient condition for inequalities between the time and customer averages of the system if the state of the system between arrival epochs is stochastically decreasing and convex and the lack of anticipation assumption is satisfied. HNB(W)UE is a wider class than NB(W)UE, being the largest of all available classes of distributions with positive (negative) aging properties. Thus, this result represents an important step beyond existing result on inequalities between time and customer averages, which states that for arrival processes, the NB(W)UE property is a sufficient condition for inequalities.","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140200586","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 results for sums and extremes 和与极值的渐近结果
IF 1 4区 数学
Journal of Applied Probability Pub Date : 2024-03-13 DOI: 10.1017/jpr.2023.118
Rita Giuliano, Claudio Macci, Barbara Pacchiarotti
{"title":"Asymptotic results for sums and extremes","authors":"Rita Giuliano, Claudio Macci, Barbara Pacchiarotti","doi":"10.1017/jpr.2023.118","DOIUrl":"https://doi.org/10.1017/jpr.2023.118","url":null,"abstract":"<p>The term <span>moderate deviations</span> is often used in the literature to mean a class of large deviation principles that, in some sense, fills the gap between a convergence in probability of some random variables to a constant, and a weak convergence to a centered Gaussian distribution (when such random variables are properly centered and rescaled). We talk about <span>noncentral moderate deviations</span> when the weak convergence is towards a non-Gaussian distribution. In this paper we prove a noncentral moderate deviation result for the bivariate sequence of sums and maxima of independent and identically distributed random variables bounded from above. We also prove a result where the random variables are not bounded from above, and the maxima are suitably normalized. Finally, we prove a moderate deviation result for sums of partial minima of independent and identically distributed <span>exponential</span> random variables.</p>","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140115903","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
Color-avoiding percolation and branching processes 避色渗流和分支过程
IF 1 4区 数学
Journal of Applied Probability Pub Date : 2024-03-08 DOI: 10.1017/jpr.2023.115
Panna Tímea Fekete, Roland Molontay, Balázs Ráth, Kitti Varga
{"title":"Color-avoiding percolation and branching processes","authors":"Panna Tímea Fekete, Roland Molontay, Balázs Ráth, Kitti Varga","doi":"10.1017/jpr.2023.115","DOIUrl":"https://doi.org/10.1017/jpr.2023.115","url":null,"abstract":"We study a variant of the color-avoiding percolation model introduced by Krause <jats:italic>et al.</jats:italic>, namely we investigate the color-avoiding bond percolation setup on (not necessarily properly) edge-colored Erdős–Rényi random graphs. We say that two vertices are color-avoiding connected in an edge-colored graph if, after the removal of the edges of any color, they are in the same component in the remaining graph. The color-avoiding connected components of an edge-colored graph are maximal sets of vertices such that any two of them are color-avoiding connected. We consider the fraction of vertices contained in color-avoiding connected components of a given size, as well as the fraction of vertices contained in the giant color-avoidin g connected component. It is known that these quantities converge, and the limits can be expressed in terms of probabilities associated to edge-colored branching process trees. We provide explicit formulas for the limit of the fraction of vertices contained in the giant color-avoiding connected component, and we give a simpler asymptotic expression for it in the barely supercritical regime. In addition, in the two-colored case we also provide explicit formulas for the limit of the fraction of vertices contained in color-avoiding connected components of a given size.","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140075069","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
Skew Ornstein–Uhlenbeck processes with sticky reflection and their applications to bond pricing 具有粘性反射的倾斜奥恩斯坦-乌伦贝克过程及其在债券定价中的应用
IF 1 4区 数学
Journal of Applied Probability Pub Date : 2024-03-06 DOI: 10.1017/jpr.2023.110
Shiyu Song, Guangli Xu
{"title":"Skew Ornstein–Uhlenbeck processes with sticky reflection and their applications to bond pricing","authors":"Shiyu Song, Guangli Xu","doi":"10.1017/jpr.2023.110","DOIUrl":"https://doi.org/10.1017/jpr.2023.110","url":null,"abstract":"<p>We study a skew Ornstein–Uhlenbeck process with zero being a sticky reflecting boundary, which is defined as the weak solution to a stochastic differential equation (SDE) system involving local time. The main results obtained include: (i) the existence and uniqueness of solutions to the SDE system, (ii) the scale function and speed measure, and (iii) the distributional properties regarding the transition density and the first hitting times. On the application side, we apply the process to interest rate modeling and obtain the explicit pricing formula for zero-coupon bonds. Numerical examples illustrate the impacts on bond yields of skewness and stickiness parameters.</p>","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140043941","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
Average Jaccard index of random graphs 随机图的平均杰卡尔指数
IF 1 4区 数学
Journal of Applied Probability Pub Date : 2024-02-26 DOI: 10.1017/jpr.2023.112
Qunqiang Feng, Shuai Guo, Zhishui Hu
{"title":"Average Jaccard index of random graphs","authors":"Qunqiang Feng, Shuai Guo, Zhishui Hu","doi":"10.1017/jpr.2023.112","DOIUrl":"https://doi.org/10.1017/jpr.2023.112","url":null,"abstract":"The asymptotic behavior of the Jaccard index in <jats:italic>G</jats:italic>(<jats:italic>n</jats:italic>, <jats:italic>p</jats:italic>), the classical Erdös–Rényi random graph model, is studied as <jats:italic>n</jats:italic> goes to infinity. We first derive the asymptotic distribution of the Jaccard index of any pair of distinct vertices, as well as the first two moments of this index. Then the average of the Jaccard indices over all vertex pairs in <jats:italic>G</jats:italic>(<jats:italic>n</jats:italic>, <jats:italic>p</jats:italic>) is shown to be asymptotically normal under an additional mild condition that <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900223001122_inline1.png\" /> <jats:tex-math> $nptoinfty$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> and <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900223001122_inline2.png\" /> <jats:tex-math> $n^2(1-p)toinfty$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>.","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139979356","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 -ary tree algorithms with successive interference cancellation 具有连续干扰消除功能的 -ary 树算法分析
IF 1 4区 数学
Journal of Applied Probability Pub Date : 2024-02-26 DOI: 10.1017/jpr.2023.107
Quirin Vogel, Yash Deshpande, Cedomir Stefanović, Wolfgang Kellerer
{"title":"Analysis of -ary tree algorithms with successive interference cancellation","authors":"Quirin Vogel, Yash Deshpande, Cedomir Stefanović, Wolfgang Kellerer","doi":"10.1017/jpr.2023.107","DOIUrl":"https://doi.org/10.1017/jpr.2023.107","url":null,"abstract":"We calculate the mean throughput, number of collisions, successes, and idle slots for random tree algorithms with successive interference cancellation. Except for the case of the throughput for the binary tree, all the results are new. We furthermore disprove the claim that only the binary tree maximizes throughput. Our method works with many observables and can be used as a blueprint for further analysis.","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139979054","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
Connectivity of random graphs after centrality-based vertex removal 基于中心性的顶点移除后随机图的连接性
IF 1 4区 数学
Journal of Applied Probability Pub Date : 2024-02-23 DOI: 10.1017/jpr.2023.106
Remco van der Hofstad, Manish Pandey
{"title":"Connectivity of random graphs after centrality-based vertex removal","authors":"Remco van der Hofstad, Manish Pandey","doi":"10.1017/jpr.2023.106","DOIUrl":"https://doi.org/10.1017/jpr.2023.106","url":null,"abstract":"Centrality measures aim to indicate who is important in a network. Various notions of ‘being important’ give rise to different centrality measures. In this paper, we study how important the central vertices are for the <jats:italic>connectivity structure</jats:italic> of the network, by investigating how the removal of the most central vertices affects the number of connected components and the size of the giant component. We use <jats:italic>local convergence techniques</jats:italic> to identify the limiting number of connected components for locally converging graphs and centrality measures that depend on the vertex’s neighbourhood. For the size of the giant, we prove a general upper bound. For the matching lower bound, we specialise to the case of <jats:italic>degree centrality</jats:italic> on one of the most popular models in network science, the <jats:italic>configuration model</jats:italic>, for which we show that removal of the highest-degree vertices destroys the giant most.","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139955154","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
Continuous dependence of stationary distributions on parameters for stochastic predator–prey models 捕食者-猎物随机模型的静态分布对参数的连续依赖性
IF 1 4区 数学
Journal of Applied Probability Pub Date : 2024-02-22 DOI: 10.1017/jpr.2023.98
Nguyen Duc Toan, Nguyen Thanh Dieu, Nguyen Huu Du, Le Ba Dung
{"title":"Continuous dependence of stationary distributions on parameters for stochastic predator–prey models","authors":"Nguyen Duc Toan, Nguyen Thanh Dieu, Nguyen Huu Du, Le Ba Dung","doi":"10.1017/jpr.2023.98","DOIUrl":"https://doi.org/10.1017/jpr.2023.98","url":null,"abstract":"<p>This research studies the robustness of permanence and the continuous dependence of the stationary distribution on the parameters for a stochastic predator–prey model with Beddington–DeAngelis functional response. We show that if the model is extinct (resp. permanent) for a parameter, it is still extinct (resp. permanent) in a neighbourhood of this parameter. In the case of extinction, the Lyapunov exponent of predator quantity is negative and the prey quantity converges almost to the saturated situation, where the predator is absent at an exponential rate. Under the condition of permanence, the unique stationary distribution converges weakly to the degenerate measure concentrated at the unique limit cycle or at the globally asymptotic equilibrium when the diffusion term tends to 0.</p>","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139924463","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
JPR volume 61 issue 1 Cover and Back matter 日本期刊》第 61 卷第 1 期封面和封底
IF 1 4区 数学
Journal of Applied Probability Pub Date : 2024-02-16 DOI: 10.1017/jpr.2024.3
{"title":"JPR volume 61 issue 1 Cover and Back matter","authors":"","doi":"10.1017/jpr.2024.3","DOIUrl":"https://doi.org/10.1017/jpr.2024.3","url":null,"abstract":"","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139962453","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
Applied Probability Trust prizes 2023 2023 年应用概率信托奖
IF 1 4区 数学
Journal of Applied Probability Pub Date : 2024-02-16 DOI: 10.1017/jpr.2024.6
{"title":"Applied Probability Trust prizes 2023","authors":"","doi":"10.1017/jpr.2024.6","DOIUrl":"https://doi.org/10.1017/jpr.2024.6","url":null,"abstract":"","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139961175","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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