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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":"295 1","pages":""},"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":"42 1","pages":""},"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":"34 1","pages":""},"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
Inference on the intraday spot volatility from high-frequency order prices with irregular microstructure noise 从具有不规则微观结构噪声的高频订单价格推断日内现货波动率
IF 1 4区 数学
Journal of Applied Probability Pub Date : 2024-02-14 DOI: 10.1017/jpr.2023.96
Markus Bibinger
{"title":"Inference on the intraday spot volatility from high-frequency order prices with irregular microstructure noise","authors":"Markus Bibinger","doi":"10.1017/jpr.2023.96","DOIUrl":"https://doi.org/10.1017/jpr.2023.96","url":null,"abstract":"We consider estimation of the spot volatility in a stochastic boundary model with one-sided microstructure noise for high-frequency limit order prices. Based on discrete, noisy observations of an Itô semimartingale with jumps and general stochastic volatility, we present a simple and explicit estimator using local order statistics. We establish consistency and stable central limit theorems as asymptotic properties. The asymptotic analysis builds upon an expansion of tail probabilities for the order statistics based on a generalized arcsine law. In order to use the involved distribution of local order statistics for a bias correction, an efficient numerical algorithm is developed. We demonstrate the finite-sample performance of the estimation in a Monte Carlo simulation.","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":"14 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139764744","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
On some semi-parametric estimates for European option prices 关于欧洲期权价格的一些半参数估计
IF 1 4区 数学
Journal of Applied Probability Pub Date : 2024-02-14 DOI: 10.1017/jpr.2023.94
Carlo Marinelli
{"title":"On some semi-parametric estimates for European option prices","authors":"Carlo Marinelli","doi":"10.1017/jpr.2023.94","DOIUrl":"https://doi.org/10.1017/jpr.2023.94","url":null,"abstract":"We show that an estimate by de la Peña, Ibragimov, and Jordan for <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900223000943_inline1.png\" /> <jats:tex-math> ${mathbb{E}}(X-c)^+$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>, with <jats:italic>c</jats:italic> a constant and <jats:italic>X</jats:italic> a random variable of which the mean, the variance, and <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900223000943_inline2.png\" /> <jats:tex-math> $mathbb{P}(X leqslant c)$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> are known, implies an estimate by Scarf on the infimum of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900223000943_inline3.png\" /> <jats:tex-math> ${mathbb{E}}(X wedge c)$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> over the set of positive random variables <jats:italic>X</jats:italic> with fixed mean and variance. This also shows, as a consequence, that the former estimate implies an estimate by Lo on European option prices.","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":"10 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139764766","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
An exponential nonuniform Berry–Esseen bound of the maximum likelihood estimator in a Jacobi process 雅可比过程中最大似然估计子的指数非均匀贝里-埃森边界
IF 1 4区 数学
Journal of Applied Probability Pub Date : 2024-02-14 DOI: 10.1017/jpr.2023.100
Hui Jiang, Qihao Lin, Shaochen Wang
{"title":"An exponential nonuniform Berry–Esseen bound of the maximum likelihood estimator in a Jacobi process","authors":"Hui Jiang, Qihao Lin, Shaochen Wang","doi":"10.1017/jpr.2023.100","DOIUrl":"https://doi.org/10.1017/jpr.2023.100","url":null,"abstract":"We establish the exponential nonuniform Berry–Esseen bound for the maximum likelihood estimator of unknown drift parameter in an ultraspherical Jacobi process using the change of measure method and precise asymptotic analysis techniques. As applications, the optimal uniform Berry–Esseen bound and optimal Cramér-type moderate deviation for the corresponding maximum likelihood estimator are obtained.","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":"14 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139764734","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
Scaling limit of the local time of random walks conditioned to stay positive 以保持正值为条件的随机游走局部时间的缩放极限
IF 1 4区 数学
Journal of Applied Probability Pub Date : 2024-02-13 DOI: 10.1017/jpr.2023.102
Wenming Hong, Mingyang Sun
{"title":"Scaling limit of the local time of random walks conditioned to stay positive","authors":"Wenming Hong, Mingyang Sun","doi":"10.1017/jpr.2023.102","DOIUrl":"https://doi.org/10.1017/jpr.2023.102","url":null,"abstract":"We prove that the local time of random walks conditioned to stay positive converges to the corresponding local time of three-dimensional Bessel processes by proper scaling. Our proof is based on Tanaka’s pathwise construction for conditioned random walks and the derivation of asymptotics for mixed moments of the local time.","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":"39 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139764908","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
De Finetti’s control problem with a concave bound on the control rate 德菲内蒂控制问题与控制率的凹约束
IF 1 4区 数学
Journal of Applied Probability Pub Date : 2024-01-25 DOI: 10.1017/jpr.2023.87
Félix Locas, Jean-François Renaud
{"title":"De Finetti’s control problem with a concave bound on the control rate","authors":"Félix Locas, Jean-François Renaud","doi":"10.1017/jpr.2023.87","DOIUrl":"https://doi.org/10.1017/jpr.2023.87","url":null,"abstract":"<p>We consider De Finetti’s control problem for absolutely continuous strategies with control rates bounded by a concave function and prove that a generalized mean-reverting strategy is optimal in a Brownian model. In order to solve this problem, we need to deal with a nonlinear Ornstein–Uhlenbeck process. Despite the level of generality of the bound imposed on the rate, an explicit expression for the value function is obtained up to the evaluation of two functions. This optimal control problem has, as special cases, those solved in Jeanblanc-Picqué and Shiryaev (1995) and Renaud and Simard (2021) when the control rate is bounded by a constant and a linear function, respectively.</p>","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":"14 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139552603","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
Approximation with ergodic processes and testability 用遍历过程逼近和可测试性
IF 1 4区 数学
Journal of Applied Probability Pub Date : 2024-01-23 DOI: 10.1017/jpr.2023.89
Isaac Loh
{"title":"Approximation with ergodic processes and testability","authors":"Isaac Loh","doi":"10.1017/jpr.2023.89","DOIUrl":"https://doi.org/10.1017/jpr.2023.89","url":null,"abstract":"We show that stationary time series can be uniformly approximated over all finite time intervals by mixing, non-ergodic, non-mean-ergodic, and periodic processes, and by codings of aperiodic processes. A corollary is that the ergodic hypothesis—that time averages will converge to their statistical counterparts—and several adjacent hypotheses are not testable in the non-parametric case. Further Baire category implications are also explored.","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":"10 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139552429","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
SIR model with social gatherings 有社交聚会的 SIR 模式
IF 1 4区 数学
Journal of Applied Probability Pub Date : 2024-01-15 DOI: 10.1017/jpr.2023.65
Roberto Cortez
{"title":"SIR model with social gatherings","authors":"Roberto Cortez","doi":"10.1017/jpr.2023.65","DOIUrl":"https://doi.org/10.1017/jpr.2023.65","url":null,"abstract":"<p>We introduce an extension to Kermack and McKendrick’s classic susceptible–infected–recovered (SIR) model in epidemiology, whose underlying mechanism of infection consists of individuals attending randomly generated social gatherings. This gives rise to a system of ordinary differential equations (ODEs) where the force of the infection term depends non-linearly on the proportion of infected individuals. Some specific instances yield models already studied in the literature, to which the present work provides a probabilistic foundation. The basic reproduction number is seen to depend quadratically on the average size of the gatherings, which may be helpful in understanding how restrictions on social gatherings affect the spread of the disease. We rigorously justify our model by showing that the system of ODEs is the mean-field limit of the jump Markov process corresponding to the evolution of the disease in a finite population.</p>","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":"13 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139470171","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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