Advances in Applied Probability最新文献

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Strong convergence of an epidemic model with mixing groups 混合群体流行病模型的强收敛性
IF 1.2 4区 数学
Advances in Applied Probability Pub Date : 2023-09-01 DOI: 10.1017/apr.2023.29
Frank Ball, Peter Neal
{"title":"Strong convergence of an epidemic model with mixing groups","authors":"Frank Ball, Peter Neal","doi":"10.1017/apr.2023.29","DOIUrl":"https://doi.org/10.1017/apr.2023.29","url":null,"abstract":"\u0000 We consider an SIR (susceptible \u0000 \u0000 \u0000 \u0000$to$\u0000\u0000 \u0000 infective \u0000 \u0000 \u0000 \u0000$to$\u0000\u0000 \u0000 recovered) epidemic in a closed population of size n, in which infection spreads via mixing events, comprising individuals chosen uniformly at random from the population, which occur at the points of a Poisson process. This contrasts sharply with most epidemic models, in which infection is spread purely by pairwise interaction. A sequence of epidemic processes, indexed by n, and an approximating branching process are constructed on a common probability space via embedded random walks. We show that under suitable conditions the process of infectives in the epidemic process converges almost surely to the branching process. This leads to a threshold theorem for the epidemic process, where a major outbreak is defined as one that infects at least \u0000 \u0000 \u0000 \u0000$log n$\u0000\u0000 \u0000 individuals. We show further that there exists \u0000 \u0000 \u0000 \u0000$delta gt 0$\u0000\u0000 \u0000 , depending on the model parameters, such that the probability that a major outbreak has size at least \u0000 \u0000 \u0000 \u0000$delta n$\u0000\u0000 \u0000 tends to one as \u0000 \u0000 \u0000 \u0000$n to infty$\u0000\u0000 \u0000 .","PeriodicalId":53160,"journal":{"name":"Advances in Applied Probability","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43235234","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
Adaptation of a population to a changing environment in the light of quasi-stationarity 准平稳性:根据准平稳性,种群对环境变化的适应
IF 1.2 4区 数学
Advances in Applied Probability Pub Date : 2023-08-30 DOI: 10.1017/apr.2023.28
Aurélien Velleret
{"title":"Adaptation of a population to a changing environment in the light of quasi-stationarity","authors":"Aurélien Velleret","doi":"10.1017/apr.2023.28","DOIUrl":"https://doi.org/10.1017/apr.2023.28","url":null,"abstract":"\u0000 We analyze the long-term stability of a stochastic model designed to illustrate the adaptation of a population to variation in its environment. A piecewise deterministic process modeling adaptation is coupled to a Feller logistic diffusion modeling population size. As the individual features in the population become further away from the optimal ones, the growth rate declines, making population extinction more likely. Assuming that the environment changes deterministically and steadily in a constant direction, we obtain the existence and uniqueness of the quasi-stationary distribution, the associated survival capacity, and the Q-process. Our approach also provides several exponential convergence results (in total variation for the measures). From this synthetic information, we can characterize the efficiency of internal adaptation (i.e. population turnover from mutant invasions). When the latter is lacking, there is still stability, but because of the high level of population extinction. Therefore, any characterization of internal adaptation should be based on specific features of this quasi-ergodic regime rather than the mere existence of the regime itself.","PeriodicalId":53160,"journal":{"name":"Advances in Applied Probability","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42308207","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
Bootstrap percolation in inhomogeneous random graphs 非齐次随机图中的自举渗流
4区 数学
Advances in Applied Probability Pub Date : 2023-08-07 DOI: 10.1017/apr.2023.21
Hamed Amini, Nikolaos Fountoulakis, Konstantinos Panagiotou
{"title":"Bootstrap percolation in inhomogeneous random graphs","authors":"Hamed Amini, Nikolaos Fountoulakis, Konstantinos Panagiotou","doi":"10.1017/apr.2023.21","DOIUrl":"https://doi.org/10.1017/apr.2023.21","url":null,"abstract":"Abstract A bootstrap percolation process on a graph with n vertices is an ‘infection’ process evolving in rounds. Let $r ge 2$ be fixed. Initially, there is a subset of infected vertices. In each subsequent round, every uninfected vertex that has at least r infected neighbors becomes infected as well and remains so forever. We consider this process in the case where the underlying graph is an inhomogeneous random graph whose kernel is of rank one. Assuming that initially every vertex is infected independently with probability $p in (0,1]$ , we provide a law of large numbers for the size of the set of vertices that are infected by the end of the process. Moreover, we investigate the case $p = p(n) = o(1)$ , and we focus on the important case of inhomogeneous random graphs exhibiting a power-law degree distribution with exponent $beta in (2,3)$ . The first two authors have shown in this setting the existence of a critical $p_c =o(1)$ such that, with high probability, if $p =o(p_c)$ , then the process does not evolve at all, whereas if $p = omega(p_c)$ , then the final set of infected vertices has size $Omega(n)$ . In this work we determine the asymptotic fraction of vertices that will eventually be infected and show that it also satisfies a law of large numbers.","PeriodicalId":53160,"journal":{"name":"Advances in Applied Probability","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135840680","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: 1
A modification of the random cutting model 随机切削模型的修正
4区 数学
Advances in Applied Probability Pub Date : 2023-08-07 DOI: 10.1017/apr.2023.22
Fabian Burghart
{"title":"A modification of the random cutting model","authors":"Fabian Burghart","doi":"10.1017/apr.2023.22","DOIUrl":"https://doi.org/10.1017/apr.2023.22","url":null,"abstract":"Abstract We propose a modification to the random destruction of graphs: given a finite network with a distinguished set of sources and targets, remove (cut) vertices at random, discarding components that do not contain a source node. We investigate the number of cuts required until all targets are removed, and the size of the remaining graph. This model interpolates between the random cutting model going back to Meir and Moon ( J. Austral. Math. Soc. 11 , 1970) and site percolation. We prove several general results, including that the size of the remaining graph is a tight family of random variables for compatible sequences of expander-type graphs, and determine limiting distributions for binary caterpillar trees and complete binary trees.","PeriodicalId":53160,"journal":{"name":"Advances in Applied Probability","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135840483","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
APR volume 55 issue 3 Cover and Front matter APR第55卷第3期封面和封面问题
IF 1.2 4区 数学
Advances in Applied Probability Pub Date : 2023-08-07 DOI: 10.1017/apr.2023.30
{"title":"APR volume 55 issue 3 Cover and Front matter","authors":"","doi":"10.1017/apr.2023.30","DOIUrl":"https://doi.org/10.1017/apr.2023.30","url":null,"abstract":"","PeriodicalId":53160,"journal":{"name":"Advances in Applied Probability","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45003409","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
APR volume 55 issue 3 Cover and Back matter APR第55卷第3期封面和封底
IF 1.2 4区 数学
Advances in Applied Probability Pub Date : 2023-08-07 DOI: 10.1017/apr.2023.31
{"title":"APR volume 55 issue 3 Cover and Back matter","authors":"","doi":"10.1017/apr.2023.31","DOIUrl":"https://doi.org/10.1017/apr.2023.31","url":null,"abstract":"","PeriodicalId":53160,"journal":{"name":"Advances in Applied Probability","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48829301","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
-Stable convergence of heavy-/light-tailed infinitely wide neural networks -重尾/轻尾无限宽神经网络的稳定收敛
IF 1.2 4区 数学
Advances in Applied Probability Pub Date : 2023-07-03 DOI: 10.1017/apr.2023.3
Paul Jung, Hoileong Lee, Jiho Lee, Hongseok Yang
{"title":"-Stable convergence of heavy-/light-tailed infinitely wide neural networks","authors":"Paul Jung, Hoileong Lee, Jiho Lee, Hongseok Yang","doi":"10.1017/apr.2023.3","DOIUrl":"https://doi.org/10.1017/apr.2023.3","url":null,"abstract":"\u0000 We consider infinitely wide multi-layer perceptrons (MLPs) which are limits of standard deep feed-forward neural networks. We assume that, for each layer, the weights of an MLP are initialized with independent and identically distributed (i.i.d.) samples from either a light-tailed (finite-variance) or a heavy-tailed distribution in the domain of attraction of a symmetric \u0000 \u0000 \u0000 \u0000$alpha$\u0000\u0000 \u0000 -stable distribution, where \u0000 \u0000 \u0000 \u0000$alphain(0,2]$\u0000\u0000 \u0000 may depend on the layer. For the bias terms of the layer, we assume i.i.d. initializations with a symmetric \u0000 \u0000 \u0000 \u0000$alpha$\u0000\u0000 \u0000 -stable distribution having the same \u0000 \u0000 \u0000 \u0000$alpha$\u0000\u0000 \u0000 parameter as that layer. Non-stable heavy-tailed weight distributions are important since they have been empirically seen to emerge in trained deep neural nets such as the ResNet and VGG series, and proven to naturally arise via stochastic gradient descent. The introduction of heavy-tailed weights broadens the class of priors in Bayesian neural networks. In this work we extend a recent result of Favaro, Fortini, and Peluchetti (2020) to show that the vector of pre-activation values at all nodes of a given hidden layer converges in the limit, under a suitable scaling, to a vector of i.i.d. random variables with symmetric \u0000 \u0000 \u0000 \u0000$alpha$\u0000\u0000 \u0000 -stable distributions, \u0000 \u0000 \u0000 \u0000$alphain(0,2]$\u0000\u0000 \u0000 .","PeriodicalId":53160,"journal":{"name":"Advances in Applied Probability","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47692607","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 Monte Carlo algorithm for the extrema of tempered stable processes 回火稳定过程极值的蒙特卡罗算法
IF 1.2 4区 数学
Advances in Applied Probability Pub Date : 2023-06-30 DOI: 10.1017/apr.2023.1
J. G. González Cázares, Aleksandar Mijatovi'c
{"title":"A Monte Carlo algorithm for the extrema of tempered stable processes","authors":"J. G. González Cázares, Aleksandar Mijatovi'c","doi":"10.1017/apr.2023.1","DOIUrl":"https://doi.org/10.1017/apr.2023.1","url":null,"abstract":"\u0000 We develop a novel Monte Carlo algorithm for the vector consisting of the supremum, the time at which the supremum is attained, and the position at a given (constant) time of an exponentially tempered Lévy process. The algorithm, based on the increments of the process without tempering, converges geometrically fast (as a function of the computational cost) for discontinuous and locally Lipschitz functions of the vector. We prove that the corresponding multilevel Monte Carlo estimator has optimal computational complexity (i.e. of order \u0000 \u0000 \u0000 \u0000$varepsilon^{-2}$\u0000\u0000 \u0000 if the mean squared error is at most \u0000 \u0000 \u0000 \u0000$varepsilon^2$\u0000\u0000 \u0000 ) and provide its central limit theorem (CLT). Using the CLT we construct confidence intervals for barrier option prices and various risk measures based on drawdown under the tempered stable (CGMY) model calibrated/estimated on real-world data. We provide non-asymptotic and asymptotic comparisons of our algorithm with existing approximations, leading to rule-of-thumb principles guiding users to the best method for a given set of parameters. We illustrate the performance of the algorithm with numerical examples.","PeriodicalId":53160,"journal":{"name":"Advances in Applied Probability","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41909126","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: 3
Ordering and ageing properties of developed sequential order statistics governed by the Archimedean copula 阿基米德copula控制的发展序列序统计量的有序性和老化性
IF 1.2 4区 数学
Advances in Applied Probability Pub Date : 2023-06-26 DOI: 10.1017/apr.2023.25
Tanmay Sahoo, Nil Kamal Hazra
{"title":"Ordering and ageing properties of developed sequential order statistics governed by the Archimedean copula","authors":"Tanmay Sahoo, Nil Kamal Hazra","doi":"10.1017/apr.2023.25","DOIUrl":"https://doi.org/10.1017/apr.2023.25","url":null,"abstract":"\u0000 Developed sequential order statistics (DSOS) are very useful in modeling the lifetimes of systems with dependent components, where the failure of one component affects the performance of remaining surviving components. We study some stochastic comparison results for DSOS in both one-sample and two-sample scenarios. Furthermore, we study various ageing properties of DSOS. We state many useful results for generalized order statistics as well as ordinary order statistics with dependent random variables. At the end, some numerical examples are given to illustrate the proposed results.","PeriodicalId":53160,"journal":{"name":"Advances in Applied Probability","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44711617","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: 1
Conditions for indexability of restless bandits and an algorithm to compute whittle index – CORRIGENDUM 不安分土匪可指数化的条件和计算whittle指数的算法——CORRIGENDUM
IF 1.2 4区 数学
Advances in Applied Probability Pub Date : 2023-06-09 DOI: 10.1017/apr.2022.77
N. Akbarzadeh, Aditya Mahajan
{"title":"Conditions for indexability of restless bandits and an algorithm to compute whittle index – CORRIGENDUM","authors":"N. Akbarzadeh, Aditya Mahajan","doi":"10.1017/apr.2022.77","DOIUrl":"https://doi.org/10.1017/apr.2022.77","url":null,"abstract":"\u0000 This note corrects an error in the formula to obtain the Whittle index using the Sherman–Morrison formula in Akbarzadeh and Mahajan (2022). Also, some other minor typos are highlighted.","PeriodicalId":53160,"journal":{"name":"Advances in Applied Probability","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41882972","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: 3
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