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An extension of Hawkes processes with ephemeral nearest effects 具有短暂最近效应的霍克斯过程的扩展
IF 0.7 4区 数学
Stochastic Models Pub Date : 2021-03-25 DOI: 10.1080/15326349.2021.1880940
L. Cui, Jingyuan Shen
{"title":"An extension of Hawkes processes with ephemeral nearest effects","authors":"L. Cui, Jingyuan Shen","doi":"10.1080/15326349.2021.1880940","DOIUrl":"https://doi.org/10.1080/15326349.2021.1880940","url":null,"abstract":"Abstract Hawkes processes have been widely studied in both theory and applications because of their self-exciting effects, but there are still some questions and room left for exploring the self-exciting point processes. In this paper, an ephemeral self-exciting Hawkes process is developed, which contains 1-memory and 0-memory self-exciting point processes. After giving the definition of the ephemeral self-exciting Hawkes process, some explanations on this new point process, properties, declustering of the occurrences of events, positive and negative self-exciting effects are presented. Moments of this point process are derived as well in the paper by using the Laplace transforms and the elementary method. Some special cases are considered and the computation methods of moments are also presented by the difference method and inverse Laplace transforms, respectively. Combining dynamics of the self-exciting point process and the delayed renewal process is an important feature of the proposed ephemeral self-exciting Hawkes process, which may shed light on the related studies in the future.","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":"37 1","pages":"335 - 366"},"PeriodicalIF":0.7,"publicationDate":"2021-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/15326349.2021.1880940","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45220181","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
Fractional Poisson random sum and its associated normal variance mixture 分数阶泊松随机和及其相关的正态方差混合
IF 0.7 4区 数学
Stochastic Models Pub Date : 2021-03-09 DOI: 10.1080/15326349.2021.1954533
Gabriela Oliveira, W. Barreto‐Souza, Roger W. C. Silva
{"title":"Fractional Poisson random sum and its associated normal variance mixture","authors":"Gabriela Oliveira, W. Barreto‐Souza, Roger W. C. Silva","doi":"10.1080/15326349.2021.1954533","DOIUrl":"https://doi.org/10.1080/15326349.2021.1954533","url":null,"abstract":"Abstract In this work, we study the partial sums of independent and identically distributed random variables with the number of terms following a fractional Poisson (FP) distribution. The FP sum contains the Poisson and geometric summations as particular cases. We show that the weak limit of the FP summation, when properly normalized, is a mixture between the normal and Mittag-Leffler distributions, which we call by Normal-Mittag-Leffler (NML) law. A parameter estimation procedure for the NML distribution is developed and the associated asymptotic distribution is derived. Simulations are run to check the performance of the proposed estimators under finite samples. An empirical illustration on the daily log-returns of the Brazilian stock exchange index (IBOVESPA) shows that the NML distribution captures better the tails than some of its competitors. Related problems such as a mixed Poisson representation for the FP law and the weak convergence for the Conway-Maxwell-Poisson random sum are also addressed.","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":"37 1","pages":"654 - 678"},"PeriodicalIF":0.7,"publicationDate":"2021-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/15326349.2021.1954533","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45409165","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: 2
Continuous scaled phase-type distributions 连续比例相位类型分布
IF 0.7 4区 数学
Stochastic Models Pub Date : 2021-03-03 DOI: 10.1080/15326349.2022.2089683
Hansjoerg Albrecher, Martin Bladt, M. Bladt, Jorge Yslas
{"title":"Continuous scaled phase-type distributions","authors":"Hansjoerg Albrecher, Martin Bladt, M. Bladt, Jorge Yslas","doi":"10.1080/15326349.2022.2089683","DOIUrl":"https://doi.org/10.1080/15326349.2022.2089683","url":null,"abstract":"Abstract Products between phase-type distributed random variables and any independent, positive and continuous random variable are studied. Their asymptotic properties are established, and an expectation-maximization algorithm for their effective statistical inference is derived and implemented using real-world datasets. In contrast to discrete scaling studied in earlier literature, in the present continuous case closed-form formulas for various functionals of the resulting distributions are obtained, which facilitates both their analysis and implementation. The resulting mixture distributions are very often heavy-tailed and yet retain various properties of phase-type distributions, such as being dense (in weak convergence) on the set of distributions with positive support.","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":"39 1","pages":"293 - 322"},"PeriodicalIF":0.7,"publicationDate":"2021-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45582256","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
Adding edge dynamics to bipartite random-access networks 在二部分随机接入网络中添加边缘动态
IF 0.7 4区 数学
Stochastic Models Pub Date : 2021-02-09 DOI: 10.1080/15326349.2022.2074459
Matteo Sfragara
{"title":"Adding edge dynamics to bipartite random-access networks","authors":"Matteo Sfragara","doi":"10.1080/15326349.2022.2074459","DOIUrl":"https://doi.org/10.1080/15326349.2022.2074459","url":null,"abstract":"Abstract We consider random-access networks with nodes representing transmitter-receiver pairs whose signals interfere with each other depending on their vicinity. Data packets arrive at the nodes over time and form queues. The nodes can be either active or inactive: a node deactivates at unit rate, while it activates at a rate that depends on its queue length, provided none of its neighbors is active. In order to model the effects of user mobility in wireless networks, we analyze dynamic interference graphs where the edges are allowed to appear and disappear over time. We focus on bipartite graphs and study the transition time between the two states where one part of the network is active and the other part is inactive, in the limit as the queue lengths become large. Depending on the speed of the dynamics, we are able to obtain a rough classification of the effects of the dynamics on the transition time.","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":"38 1","pages":"545 - 581"},"PeriodicalIF":0.7,"publicationDate":"2021-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49662746","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
Correction note to “A multidimensional ruin problem and an associated notion of duality,” Stochastic Models, 32 (2016) 539–574 对“多维破产问题和对偶性的相关概念”的更正说明，随机模型，32（2016）539-574
IF 0.7 4区 数学
Stochastic Models Pub Date : 2020-12-21 DOI: 10.1080/15326349.2020.1858876
S. Ramasubramanian
{"title":"Correction note to “A multidimensional ruin problem and an associated notion of duality,” Stochastic Models, 32 (2016) 539–574","authors":"S. Ramasubramanian","doi":"10.1080/15326349.2020.1858876","DOIUrl":"https://doi.org/10.1080/15326349.2020.1858876","url":null,"abstract":"Abstract The expression given in an earlier paper for the ladder height distribution is erroneous. After deriving the correct version, the expression for ruin probability is provided.","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":"37 1","pages":"300 - 316"},"PeriodicalIF":0.7,"publicationDate":"2020-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/15326349.2020.1858876","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43304521","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
Optimality of admission control in an M∕M∕1∕N queue with varying services 具有可变服务的M / M / 1 / N队列的最优接纳控制
IF 0.7 4区 数学
Stochastic Models Pub Date : 2020-12-21 DOI: 10.1080/15326349.2020.1860090
Yan Su, Junping Li
{"title":"Optimality of admission control in an M∕M∕1∕N queue with varying services","authors":"Yan Su, Junping Li","doi":"10.1080/15326349.2020.1860090","DOIUrl":"https://doi.org/10.1080/15326349.2020.1860090","url":null,"abstract":"Abstract Motivated by communication networks, we study a single-server queue with varying service rates and multiple customers’ types. The difference between types of customers is defined by the profits contributed to the system. We show that the optimal trunk reservation policy exists and we compare the optimal control levels with different parameter values. Furthermore, when the optimal trunk reservation policy is more than one, we prove the uniqueness of the bias optimal policy.","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":"37 1","pages":"317 - 334"},"PeriodicalIF":0.7,"publicationDate":"2020-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/15326349.2020.1860090","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43798701","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
Resource competition in virtual network embedding 虚拟网络嵌入中的资源竞争
IF 0.7 4区 数学
Stochastic Models Pub Date : 2020-12-09 DOI: 10.1080/15326349.2020.1858875
Jing-Zhi Fu, B. Moran, P. Taylor, Chenchen Xing
{"title":"Resource competition in virtual network embedding","authors":"Jing-Zhi Fu, B. Moran, P. Taylor, Chenchen Xing","doi":"10.1080/15326349.2020.1858875","DOIUrl":"https://doi.org/10.1080/15326349.2020.1858875","url":null,"abstract":"Abstract We consider a virtual network (VN) embedding problem on a large-scale substrate physical network. We permit varying capacities and cost rates, and reservation of resources (physical links and nodes) for more profitable later VN requests. Our aim is to maximize the long-run average revenue by controlling the allocation of physical components to arriving VN requests. We propose an index policy that selects, according to state-dependent indices, a set of available physical components for each arrival. The indices are calculated in closed form requiring only intrinsic off-line information about physical components and physical resource requirements. Under reasonable assumptions related to rapidly increasing demands for VNs and resource competition, we show that this proposed policy is asymptotically optimal when the lifespans of embedded virtual components are exponentially distributed. Extensive numerical results demonstrate that the long-run average revenue earned by the proposed index policy rapidly approaches optimality: performance deviations between the index policy and the optimal solution are less than 5% in most of our simulations even for relatively small systems. Our numerical results also indicate that the long-run performance of this policy is relatively insensitive to the form of the lifespan distributions.","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":"37 1","pages":"231 - 263"},"PeriodicalIF":0.7,"publicationDate":"2020-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/15326349.2020.1858875","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48850130","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
The stochastic Leibniz formula for Volterra integrals under enlarged filtrations Volterra积分在放大滤波下的随机Leibniz公式
IF 0.7 4区 数学
Stochastic Models Pub Date : 2020-11-10 DOI: 10.2139/ssrn.3308400
M. Hess
{"title":"The stochastic Leibniz formula for Volterra integrals under enlarged filtrations","authors":"M. Hess","doi":"10.2139/ssrn.3308400","DOIUrl":"https://doi.org/10.2139/ssrn.3308400","url":null,"abstract":"We derive stochastic Leibniz formulas for Volterra integrals under enlarged filtrations. We investigate both pure-jump and Brownian Volterra processes under diverse initially enlarged filtration approaches. In these settings, we compare the ordinary with the stochastic (Doleans-Dade) exponential of a Volterra process and provide the corresponding martingale conditions. We also consider backward stochastic Volterra integral equations (BSVIEs) under enlarged filtrations and obtain the related solution formulas. We finally propose an anticipative Heath Jarrow Morton (HJM) forward rate model of Volterra-type. In an introductory section, we compile various facts on deterministic and stochastic Leibniz formulas for parameter integrals.","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2020-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45237476","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
Matrix-analytic methods for the analysis of stochastic fluid-fluid models 随机流体-流体模型分析的矩阵解析方法
IF 0.7 4区 数学
Stochastic Models Pub Date : 2020-10-25 DOI: 10.1080/15326349.2022.2049823
N. Bean, M. O’Reilly, Z. Palmowski
{"title":"Matrix-analytic methods for the analysis of stochastic fluid-fluid models","authors":"N. Bean, M. O’Reilly, Z. Palmowski","doi":"10.1080/15326349.2022.2049823","DOIUrl":"https://doi.org/10.1080/15326349.2022.2049823","url":null,"abstract":"Abstract Stochastic fluid-fluid models (SFFMs) offer powerful modeling ability for a wide range of real-life systems of significance. The existing theoretical framework for this class of models is in terms of operator-analytic methods. For the first time, we establish matrix-analytic methods for the efficient analysis of SFFMs. We illustrate the theory with numerical examples.","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":"38 1","pages":"416 - 461"},"PeriodicalIF":0.7,"publicationDate":"2020-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48201688","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
Parameter estimation for multivariate population processes: a saddlepoint approach 多元总体过程的参数估计:鞍点方法
IF 0.7 4区 数学
Stochastic Models Pub Date : 2020-10-22 DOI: 10.1080/15326349.2020.1832895
M. D. de Gunst, S. Hautphenne, M. Mandjes, Birgit Sollie
{"title":"Parameter estimation for multivariate population processes: a saddlepoint approach","authors":"M. D. de Gunst, S. Hautphenne, M. Mandjes, Birgit Sollie","doi":"10.1080/15326349.2020.1832895","DOIUrl":"https://doi.org/10.1080/15326349.2020.1832895","url":null,"abstract":"Abstract The setting considered in this paper concerns a discrete-time multivariate population process under Markov modulation. Our objective is to estimate the model parameters, based on periodic observations of the network population vector. These parameters relate to the arrival, routing and departure processes, but also to the (unobservable) Markovian background process. When opting for the classical likelihood-based approach, the evaluation of the likelihood is problematic. We show however, how an accurate saddlepoint approximation can be used. Numerical experiments illustrate our method and show that even under relatively complicated conditions the parameters are estimated relatively precisely.","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":"37 1","pages":"168 - 196"},"PeriodicalIF":0.7,"publicationDate":"2020-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/15326349.2020.1832895","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42835097","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: 2
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