Pub Date : 2023-11-16DOI: 10.1080/15326349.2023.2275298
Yuecai Han, Dingwen Zhang
In this article, we investigate the nonparametric Nadaraya-Watson estimator for the drift function of stochastic differential equations driven by fractional Brownian motion of the Hurst parameter H...
{"title":"Nadaraya-Watson estimators for stochastic differential equations driven by fractional Brownian motion","authors":"Yuecai Han, Dingwen Zhang","doi":"10.1080/15326349.2023.2275298","DOIUrl":"https://doi.org/10.1080/15326349.2023.2275298","url":null,"abstract":"In this article, we investigate the nonparametric Nadaraya-Watson estimator for the drift function of stochastic differential equations driven by fractional Brownian motion of the Hurst parameter H...","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138536258","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}
Pub Date : 2023-10-26DOI: 10.1080/15326349.2023.2267644
Hongshuai Dai, Yanhua Wu
{"title":"A queueing model with ON/OFF sources: approximation and stationarity","authors":"Hongshuai Dai, Yanhua Wu","doi":"10.1080/15326349.2023.2267644","DOIUrl":"https://doi.org/10.1080/15326349.2023.2267644","url":null,"abstract":"","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134908742","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}
Pub Date : 2023-10-19DOI: 10.1080/15326349.2023.2263538
Ji Hwan Cha, Maxim Finkelstein
Abstract.Populations of items continuously manufactured and incepted into operation are characterized by the corresponding distribution of a random age at each instant of chronological time. In this study, we consider heterogeneous populations with lifetime distributions indexed by a frailty parameter. Two approaches to defining the age composition for the described populations are described and the corresponding stochastic comparisons are considered.Keywords: Age compositionfrailtyheterogeneous populationsproduction ratestochastic comparisons2010 Mathematics Subject Classification:: 60H3 AcknowledgmentsThe authors greatly thank the reviewers for their helpful comments and advice, which have improved the presentation of this paper.Disclosure statementNo potential conflict of interest was reported by the authorsAdditional informationFundingThe work of the first author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (Grant Number: 2019R1A6A1A11051177). The work of the first author was also supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2023R1A2C1003238).
{"title":"On age composition of dynamic heterogeneous populations","authors":"Ji Hwan Cha, Maxim Finkelstein","doi":"10.1080/15326349.2023.2263538","DOIUrl":"https://doi.org/10.1080/15326349.2023.2263538","url":null,"abstract":"Abstract.Populations of items continuously manufactured and incepted into operation are characterized by the corresponding distribution of a random age at each instant of chronological time. In this study, we consider heterogeneous populations with lifetime distributions indexed by a frailty parameter. Two approaches to defining the age composition for the described populations are described and the corresponding stochastic comparisons are considered.Keywords: Age compositionfrailtyheterogeneous populationsproduction ratestochastic comparisons2010 Mathematics Subject Classification:: 60H3 AcknowledgmentsThe authors greatly thank the reviewers for their helpful comments and advice, which have improved the presentation of this paper.Disclosure statementNo potential conflict of interest was reported by the authorsAdditional informationFundingThe work of the first author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (Grant Number: 2019R1A6A1A11051177). The work of the first author was also supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2023R1A2C1003238).","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135730079","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}
Pub Date : 2023-10-17DOI: 10.1080/15326349.2023.2267663
Pierre-Yves Louis, Meghdad Mirebrahimi
AbstractThe Pólya urn is the most representative example of a reinforced stochastic process. It leads to a random (non degenerated) time-limit. The Friedman urn is a natural generalization whose almost sure (a.s.) time-limit is not random any more. In this work, in the stream of previous recent works, we introduce a new family of (finite size) systems of reinforced stochastic processes, interacting through an additional collective reinforcement of mean field type. The two reinforcement rules strengths (one component-wise, one collective) are tuned through (possibly) two different rates. In special cases, these reinforcements are of Pólya or Friedman type as in urn contexts and may thus lead to limits which may be random or not. Different parameter regimes need to be considered. We state two kind of results. First, we study the time-asymptotic and show that L2 and a.s. convergence always holds. Moreover, all the components share the same time-limit (so called synchronization phenomenon). We study the nature of the limit (random/deterministic) according to the parameters’ regime considered. Second, we study fluctuations by proving central limit theorems. Scaling coefficients vary according to the regime considered. This gives insights into many different rates of convergence. In particular, we identify the regimes where synchronization is faster than convergence toward the shared time-limit.Keywords: Almost sure convergencecentral limit theoremsfluctuationsinteracting random systemsreinforced stochastic processesstable convergencesynchronization2010 Mathematics Subject Classification: Primary 60K35Primary 60F1560F05Secondary 62L20Secondary 62P35 AcknowledgmentsI would like to thank Professor Pierre-Yves Louis for introducing me to the problem and for all the useful comments and discussions. I am also very grateful for extremely constructive feedback from the referee.Disclosure statementNo potential conflict of interest was reported by the author(s).
{"title":"Synchronization and fluctuations for interacting stochastic systems with individual and collective reinforcement","authors":"Pierre-Yves Louis, Meghdad Mirebrahimi","doi":"10.1080/15326349.2023.2267663","DOIUrl":"https://doi.org/10.1080/15326349.2023.2267663","url":null,"abstract":"AbstractThe Pólya urn is the most representative example of a reinforced stochastic process. It leads to a random (non degenerated) time-limit. The Friedman urn is a natural generalization whose almost sure (a.s.) time-limit is not random any more. In this work, in the stream of previous recent works, we introduce a new family of (finite size) systems of reinforced stochastic processes, interacting through an additional collective reinforcement of mean field type. The two reinforcement rules strengths (one component-wise, one collective) are tuned through (possibly) two different rates. In special cases, these reinforcements are of Pólya or Friedman type as in urn contexts and may thus lead to limits which may be random or not. Different parameter regimes need to be considered. We state two kind of results. First, we study the time-asymptotic and show that L2 and a.s. convergence always holds. Moreover, all the components share the same time-limit (so called synchronization phenomenon). We study the nature of the limit (random/deterministic) according to the parameters’ regime considered. Second, we study fluctuations by proving central limit theorems. Scaling coefficients vary according to the regime considered. This gives insights into many different rates of convergence. In particular, we identify the regimes where synchronization is faster than convergence toward the shared time-limit.Keywords: Almost sure convergencecentral limit theoremsfluctuationsinteracting random systemsreinforced stochastic processesstable convergencesynchronization2010 Mathematics Subject Classification: Primary 60K35Primary 60F1560F05Secondary 62L20Secondary 62P35 AcknowledgmentsI would like to thank Professor Pierre-Yves Louis for introducing me to the problem and for all the useful comments and discussions. I am also very grateful for extremely constructive feedback from the referee.Disclosure statementNo potential conflict of interest was reported by the author(s).","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135944106","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}
Pub Date : 2023-10-11DOI: 10.1080/15326349.2023.2253278
Liangxue Li, Xuejun Wang, Chen Yi
Abstract.In this article, we establish the complete f-moment convergence for a class of random variables satisfying a Rosenthal-type maximal inequality and a weak mean dominating condition with a mean dominating variable. As corollaries, the complete moment convergence and complete convergence for a class of random variables are also obtained. In addition, an application of main results to nonparametric regression models is provided. Finally, we provide a numerical simulation to verify the validity of our theoretical results based on finite samples.Keywords: Complete consistencycomplete f-moment convergencenonparametric regression modelsRosenthal-type maximal inequalityMSC:: 60F1562G20 AcknowledgmentsThe authors are most grateful to the Editor and anonymous referee for carefully reading the manuscript and valuable suggestions which helped in improving an earlier version of this paper.Disclosure statementNo potential conflict of interest was reported by the authors.Additional informationFunding Supported by the National Social Science Foundation of China (22BTJ059).
{"title":"Complete <i>f</i> -moment convergence for a class of random variables with related statistical applications","authors":"Liangxue Li, Xuejun Wang, Chen Yi","doi":"10.1080/15326349.2023.2253278","DOIUrl":"https://doi.org/10.1080/15326349.2023.2253278","url":null,"abstract":"Abstract.In this article, we establish the complete f-moment convergence for a class of random variables satisfying a Rosenthal-type maximal inequality and a weak mean dominating condition with a mean dominating variable. As corollaries, the complete moment convergence and complete convergence for a class of random variables are also obtained. In addition, an application of main results to nonparametric regression models is provided. Finally, we provide a numerical simulation to verify the validity of our theoretical results based on finite samples.Keywords: Complete consistencycomplete f-moment convergencenonparametric regression modelsRosenthal-type maximal inequalityMSC:: 60F1562G20 AcknowledgmentsThe authors are most grateful to the Editor and anonymous referee for carefully reading the manuscript and valuable suggestions which helped in improving an earlier version of this paper.Disclosure statementNo potential conflict of interest was reported by the authors.Additional informationFunding Supported by the National Social Science Foundation of China (22BTJ059).","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136097651","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}
Pub Date : 2023-09-22DOI: 10.1080/15326349.2023.2256825
Arnaud Rousselle, Ercan Sönmez
AbstractThe object of study is a soft random geometric graph with vertices given by a Poisson point process on a line and edges between vertices present with probability that has a polynomial decay in the distance between them. Various aspects of such models related to connectivity structures have been studied extensively. In this article, we study the random graph from the perspective of extreme value theory and focus on the occurrence of single long edges. The model we investigate has non-periodic boundary and is parameterized by a positive constant α, which is the power for the polynomial decay of the probabilities determining the presence of an edge. As a main result, we provide a precise description of the magnitude of the longest edge in terms of asymptotic behavior in distribution. Thereby we illustrate a crucial dependence on the power α and we recover a phase transition which coincides with exactly the same phases in Benjamini and Berger[ Citation2].Keywords: Extreme value theorymaximum edge-lengthPoisson approximationrandom graphssoft random geometric graphMSC: Primary: 05C8060G70Secondary: 60F0505C8282B21 Disclosure statementNo potential conflict of interest was reported by the authors.Additional informationFundingThe IMB receives support from the EIPHI Graduate School (contract ANR-17-EURE-0002).
{"title":"The longest edge of the one-dimensional soft random geometric graph with boundaries","authors":"Arnaud Rousselle, Ercan Sönmez","doi":"10.1080/15326349.2023.2256825","DOIUrl":"https://doi.org/10.1080/15326349.2023.2256825","url":null,"abstract":"AbstractThe object of study is a soft random geometric graph with vertices given by a Poisson point process on a line and edges between vertices present with probability that has a polynomial decay in the distance between them. Various aspects of such models related to connectivity structures have been studied extensively. In this article, we study the random graph from the perspective of extreme value theory and focus on the occurrence of single long edges. The model we investigate has non-periodic boundary and is parameterized by a positive constant α, which is the power for the polynomial decay of the probabilities determining the presence of an edge. As a main result, we provide a precise description of the magnitude of the longest edge in terms of asymptotic behavior in distribution. Thereby we illustrate a crucial dependence on the power α and we recover a phase transition which coincides with exactly the same phases in Benjamini and Berger[ Citation2].Keywords: Extreme value theorymaximum edge-lengthPoisson approximationrandom graphssoft random geometric graphMSC: Primary: 05C8060G70Secondary: 60F0505C8282B21 Disclosure statementNo potential conflict of interest was reported by the authors.Additional informationFundingThe IMB receives support from the EIPHI Graduate School (contract ANR-17-EURE-0002).","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136059022","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}
Pub Date : 2023-09-08DOI: 10.1080/15326349.2023.2250432
Ying Wang, Guanggan Chen, Pingping Wang
{"title":"Moderate deviations for stochastic Cahn-Hilliard equations with a random dynamical boundary driven by Poisson random measures","authors":"Ying Wang, Guanggan Chen, Pingping Wang","doi":"10.1080/15326349.2023.2250432","DOIUrl":"https://doi.org/10.1080/15326349.2023.2250432","url":null,"abstract":"","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45878050","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}
Pub Date : 2023-09-08DOI: 10.1080/15326349.2023.2253289
A. Mészáros, M. Telek
The moments based matrix representation of Markovian and rational arrival processes (MAP/RAPs) with full rank marginal (FRM) is provided in [14]. MAP/RAPs with reduced rank marginal (RRM) differ in essential properties from the ones with FRM [13]. The main difficulty of the moments based matrix representation of MAP/RAPs with RRM comes from the fact that the moments needed to characterize a MAP/RAPs with RRM depends on the internal structure of the MAP/RAP. In this work, we propose a general procedure for moments based matrix representation that is applicable to MAP/RAPs with both FRM and RRM, independent of their internal structures. We also show that the procedure terminates in a finite number of steps which is proportional to the order of the MAP/RAP.
{"title":"Moments based matrix representation of Markov and rational arrival processes with reduced rank marginal","authors":"A. Mészáros, M. Telek","doi":"10.1080/15326349.2023.2253289","DOIUrl":"https://doi.org/10.1080/15326349.2023.2253289","url":null,"abstract":"The moments based matrix representation of Markovian and rational arrival processes (MAP/RAPs) with full rank marginal (FRM) is provided in [14]. MAP/RAPs with reduced rank marginal (RRM) differ in essential properties from the ones with FRM [13]. The main difficulty of the moments based matrix representation of MAP/RAPs with RRM comes from the fact that the moments needed to characterize a MAP/RAPs with RRM depends on the internal structure of the MAP/RAP. In this work, we propose a general procedure for moments based matrix representation that is applicable to MAP/RAPs with both FRM and RRM, independent of their internal structures. We also show that the procedure terminates in a finite number of steps which is proportional to the order of the MAP/RAP.","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44597413","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}
Pub Date : 2023-09-04DOI: 10.1080/15326349.2023.2250418
Samira Ghanbarian, Ravi R. Mazumdar
{"title":"Mean-field fluctuations at diffusion scale in threshold-based randomized routing for processor sharing systems and applications","authors":"Samira Ghanbarian, Ravi R. Mazumdar","doi":"10.1080/15326349.2023.2250418","DOIUrl":"https://doi.org/10.1080/15326349.2023.2250418","url":null,"abstract":"","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42277820","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}
Pub Date : 2023-08-10DOI: 10.1080/15326349.2023.2241071
Xulan Huang
{"title":"Quenched weighted moments for a branching process with immigration in a random environment","authors":"Xulan Huang","doi":"10.1080/15326349.2023.2241071","DOIUrl":"https://doi.org/10.1080/15326349.2023.2241071","url":null,"abstract":"","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46655374","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}
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