Pub Date : 2023-03-06DOI: 10.1080/15326349.2023.2184832
C. Hirsch, B. Jahnel, E. Cali
Abstract We consider a hybrid spatial communication system in which mobile nodes can connect to static sinks in a bounded number of intermediate relaying hops. We describe the distribution of the connection intervals of a typical mobile node, i.e., the intervals of uninterrupted connection to the family of sinks. This is achieved in the limit of many hops, sparse sinks and growing time horizons. We identify three regimes reflecting various degrees of sink densities. Namely, (1) a regime of dense sinks, in which the limit is deterministic and given as an expectation with respect to percolation clusters, (2) a regime of sparse sinks, in which the limit depends on a random number of reachable sinks, and (3) an intermediate critical regime.
{"title":"Connection intervals in multi-scale infrastructure-augmented dynamic networks","authors":"C. Hirsch, B. Jahnel, E. Cali","doi":"10.1080/15326349.2023.2184832","DOIUrl":"https://doi.org/10.1080/15326349.2023.2184832","url":null,"abstract":"Abstract We consider a hybrid spatial communication system in which mobile nodes can connect to static sinks in a bounded number of intermediate relaying hops. We describe the distribution of the connection intervals of a typical mobile node, i.e., the intervals of uninterrupted connection to the family of sinks. This is achieved in the limit of many hops, sparse sinks and growing time horizons. We identify three regimes reflecting various degrees of sink densities. Namely, (1) a regime of dense sinks, in which the limit is deterministic and given as an expectation with respect to percolation clusters, (2) a regime of sparse sinks, in which the limit depends on a random number of reachable sinks, and (3) an intermediate critical regime.","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48851821","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 : 2023-02-28DOI: 10.1080/15326349.2023.2173233
Markus Hess
In this paper, 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 setups, we compare the ordinary with the stochastic (Doléans-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 and infer the associated bond price representation. In an introductory section, we compile various facts on deterministic and stochastic Leibniz formulas for parameter integrals.
{"title":"The stochastic Leibniz formula for Volterra integrals under enlarged filtrations","authors":"Markus Hess","doi":"10.1080/15326349.2023.2173233","DOIUrl":"https://doi.org/10.1080/15326349.2023.2173233","url":null,"abstract":"In this paper, 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 setups, we compare the ordinary with the stochastic (Doléans-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 and infer the associated bond price representation. In an introductory section, we compile various facts on deterministic and stochastic Leibniz formulas for parameter integrals.","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135678117","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 : 2023-02-15DOI: 10.1080/15326349.2023.2175869
G. Yin, Huy Nguyen
Abstract In this work, we consider a number of matrix-valued random sequences that are modulated by a discrete-time Markov chain having a finite space. Assuming that the state space of the Markov chain is large, our main effort in this paper is devoted to reducing the computation complexity. To achieve this goal, our formulation uses time-scale separation of the Markov chain. The state-space of the Markov chain is split into subspaces. Next, the states of the Markov chain in each subspace are aggregated into a “super” state. Then we normalize the matrix-valued sequences that are modulated by the two-time-scale Markov chain. Under simple conditions, we derive a scaling limit of the centered and scaled sequence by using a martingale averaging approach. The study is carried out through a functional. It is shown that the scaled and interpolated sequence converges weakly to a switching diffusion.
{"title":"Sequences of random matrices modulated by a discrete-time Markov chain*","authors":"G. Yin, Huy Nguyen","doi":"10.1080/15326349.2023.2175869","DOIUrl":"https://doi.org/10.1080/15326349.2023.2175869","url":null,"abstract":"Abstract In this work, we consider a number of matrix-valued random sequences that are modulated by a discrete-time Markov chain having a finite space. Assuming that the state space of the Markov chain is large, our main effort in this paper is devoted to reducing the computation complexity. To achieve this goal, our formulation uses time-scale separation of the Markov chain. The state-space of the Markov chain is split into subspaces. Next, the states of the Markov chain in each subspace are aggregated into a “super” state. Then we normalize the matrix-valued sequences that are modulated by the two-time-scale Markov chain. Under simple conditions, we derive a scaling limit of the centered and scaled sequence by using a martingale averaging approach. The study is carried out through a functional. It is shown that the scaled and interpolated sequence converges weakly to a switching diffusion.","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49160200","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 : 2023-01-23DOI: 10.1080/15326349.2023.2166534
Caibin Zhang, Zhibin Liang
Abstract This article studies a mean-variance portfolio selection problem for a jump-diffusion model, where the drift process is modulated by a continuous unobservable Markov chain. Since there is a constraint on wealth, we tackle this problem via the technique of martingale. We first investigate the full information case that the Markov chain can be observable, closed-form expressions not only for the optimal wealth process and optimal portfolio strategy but for the efficient frontier are derived. Then, by the filtering theory, we reduce the original partial information problem to a full information one, and the corresponding optimal results are obtained as well. Furthermore, if short selling is not allowed, we find that the solution in the full information case can be derived by transforming the problem into an equivalent one with constraint only on wealth, but this technique is not applicable anymore for the partial information case.
{"title":"Constrained mean-variance portfolio optimization for jump-diffusion process under partial information","authors":"Caibin Zhang, Zhibin Liang","doi":"10.1080/15326349.2023.2166534","DOIUrl":"https://doi.org/10.1080/15326349.2023.2166534","url":null,"abstract":"Abstract This article studies a mean-variance portfolio selection problem for a jump-diffusion model, where the drift process is modulated by a continuous unobservable Markov chain. Since there is a constraint on wealth, we tackle this problem via the technique of martingale. We first investigate the full information case that the Markov chain can be observable, closed-form expressions not only for the optimal wealth process and optimal portfolio strategy but for the efficient frontier are derived. Then, by the filtering theory, we reduce the original partial information problem to a full information one, and the corresponding optimal results are obtained as well. Furthermore, if short selling is not allowed, we find that the solution in the full information case can be derived by transforming the problem into an equivalent one with constraint only on wealth, but this technique is not applicable anymore for the partial information case.","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42145285","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 : 2023-01-23DOI: 10.1080/15326349.2023.2166962
R. Roozegar, Marjan Entezari, N. Balakrishnan, Saraleean Nadarajah
{"title":"A new mixed δ-shock model and associated reliability properties","authors":"R. Roozegar, Marjan Entezari, N. Balakrishnan, Saraleean Nadarajah","doi":"10.1080/15326349.2023.2166962","DOIUrl":"https://doi.org/10.1080/15326349.2023.2166962","url":null,"abstract":"","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41854845","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 : 2023-01-12DOI: 10.1080/15326349.2022.2162545
Liang Wang, Shuo‐Jye Wu, S. Dey, Y. Tripathi, Song Mao
Abstract Reliability analysis for a multicomponent stress-strength (MSS) model is discussed in this paper. When strength and stress variables follow generalized inverted exponential distributions (GIEDs) with common scale parameters, maximum likelihood estimate of MSS reliability is established along with associated existence and uniqueness, and approximate confidence interval is also obtained in consequence. Additionally, alternative generalized estimates are proposed for MSS reliability based on constructed pivotal quantities, and associated Monte-Carlo sampling is provided for computation. Further, classical and generalized estimates are also established under unequal strength and stress parameter case. For comparison, bootstrap confidence intervals are also provided under different cases. To compare the equivalence of the strength and stress parameters, likelihood ratio testing is presented as a complement. Finally, extensive simulation studies are carried out to assess the performance of the proposed methods, and a real data example is presented for application. The numerical results indicate that the proposed generalized methods perform better than conventional likelihood results.
{"title":"Estimation of stress-strength reliability for multicomponent system with a generalized inverted exponential distribution","authors":"Liang Wang, Shuo‐Jye Wu, S. Dey, Y. Tripathi, Song Mao","doi":"10.1080/15326349.2022.2162545","DOIUrl":"https://doi.org/10.1080/15326349.2022.2162545","url":null,"abstract":"Abstract Reliability analysis for a multicomponent stress-strength (MSS) model is discussed in this paper. When strength and stress variables follow generalized inverted exponential distributions (GIEDs) with common scale parameters, maximum likelihood estimate of MSS reliability is established along with associated existence and uniqueness, and approximate confidence interval is also obtained in consequence. Additionally, alternative generalized estimates are proposed for MSS reliability based on constructed pivotal quantities, and associated Monte-Carlo sampling is provided for computation. Further, classical and generalized estimates are also established under unequal strength and stress parameter case. For comparison, bootstrap confidence intervals are also provided under different cases. To compare the equivalence of the strength and stress parameters, likelihood ratio testing is presented as a complement. Finally, extensive simulation studies are carried out to assess the performance of the proposed methods, and a real data example is presented for application. The numerical results indicate that the proposed generalized methods perform better than conventional likelihood results.","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48109093","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 : 2023-01-09DOI: 10.1080/15326349.2022.2149554
Miaomiao Wang, Min Wang, Xuejun Wang, Fei Zhang
Abstract In this paper, we study the complete f-moment convergence for arrays of rowwise m-negatively associated random variables under some general conditions. The results obtained in the paper extend and improve some previous known ones. As an application of the main results, we present the complete consistency for the estimator in a semiparametric regression model based on m-negatively associated errors. We perform some numerical simulations to verify the validity of the theoretical results based on finite samples.
{"title":"Complete f-moment convergence for arrays of rowwise m-negatively associated random variables and its statistical applications","authors":"Miaomiao Wang, Min Wang, Xuejun Wang, Fei Zhang","doi":"10.1080/15326349.2022.2149554","DOIUrl":"https://doi.org/10.1080/15326349.2022.2149554","url":null,"abstract":"Abstract In this paper, we study the complete f-moment convergence for arrays of rowwise m-negatively associated random variables under some general conditions. The results obtained in the paper extend and improve some previous known ones. As an application of the main results, we present the complete consistency for the estimator in a semiparametric regression model based on m-negatively associated errors. We perform some numerical simulations to verify the validity of the theoretical results based on finite samples.","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41861562","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 : 2022-12-29DOI: 10.1080/15326349.2022.2155194
B. Jamshidi, Parisa Torkaman
Abstract In this article, we introduce a new model derived from Pólya–Eggenberger urn model. This model is defined by considering a delay in collecting information. The mathematical formulation of this model is done through four parameters; the number of balls in the first structure (N 0), the number of white balls in the first structure (W 0), the number of rewarded balls of the color of the ball withdrawn (a), and the length of the delay (i). As the first attempt to deal with point estimation in this model, we consider at any time one of the parameters separately as unknown conditioned to knowing the other three parameters, and find its estimation. Accordingly, we introduce a sufficient estimator for this model, and found on it, obtain the maximum likelihood estimators for each of the four parameters. In addition, moment estimators for N 0 and W 0 are calculated. Also, for the other parameters, we obtain estimators based on the correlation coefficient of consecutive withdrawals. To evaluate the performance of the obtained estimators and compare their accuracy, we apply five simulations of the delayed Pólya urn model. The simulations have been done with the software Matlab R2015b. According to the simulation study, the estimators obtained from the method of moments are preferable to maximum likelihood estimators.
{"title":"The estimation in Pólya–Eggenberger urn model with a delay","authors":"B. Jamshidi, Parisa Torkaman","doi":"10.1080/15326349.2022.2155194","DOIUrl":"https://doi.org/10.1080/15326349.2022.2155194","url":null,"abstract":"Abstract In this article, we introduce a new model derived from Pólya–Eggenberger urn model. This model is defined by considering a delay in collecting information. The mathematical formulation of this model is done through four parameters; the number of balls in the first structure (N 0), the number of white balls in the first structure (W 0), the number of rewarded balls of the color of the ball withdrawn (a), and the length of the delay (i). As the first attempt to deal with point estimation in this model, we consider at any time one of the parameters separately as unknown conditioned to knowing the other three parameters, and find its estimation. Accordingly, we introduce a sufficient estimator for this model, and found on it, obtain the maximum likelihood estimators for each of the four parameters. In addition, moment estimators for N 0 and W 0 are calculated. Also, for the other parameters, we obtain estimators based on the correlation coefficient of consecutive withdrawals. To evaluate the performance of the obtained estimators and compare their accuracy, we apply five simulations of the delayed Pólya urn model. The simulations have been done with the software Matlab R2015b. According to the simulation study, the estimators obtained from the method of moments are preferable to maximum likelihood estimators.","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41693803","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 : 2022-12-22DOI: 10.1080/15326349.2022.2155666
Wenxu Dong, Jia-ning Zhou, Biteng Xu
Abstract In this article, a stochastic SIS epidemic model with constant time delay and Holling type II incidence rate is investigated. We firstly show the existence, uniqueness, and moment boundedness of the global positive solution. Then we extend the initial value space to a complete nonnegative continuous function space and obtain the existence of invariant measures for this system. Furthermore, the analysis of the asymptotic behavior around the disease-free equilibrium is given. To demonstrate, some numerical examples are provided to illustrate our results.
{"title":"A stochastic delayed SIS epidemic model with Holling type II incidence rate","authors":"Wenxu Dong, Jia-ning Zhou, Biteng Xu","doi":"10.1080/15326349.2022.2155666","DOIUrl":"https://doi.org/10.1080/15326349.2022.2155666","url":null,"abstract":"Abstract In this article, a stochastic SIS epidemic model with constant time delay and Holling type II incidence rate is investigated. We firstly show the existence, uniqueness, and moment boundedness of the global positive solution. Then we extend the initial value space to a complete nonnegative continuous function space and obtain the existence of invariant measures for this system. Furthermore, the analysis of the asymptotic behavior around the disease-free equilibrium is given. To demonstrate, some numerical examples are provided to illustrate our results.","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43853356","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 : 2022-12-07DOI: 10.1080/15326349.2022.2149555
Y. Tamura, S. Yamada
{"title":"Maintenance effort expense modeling based on cyclic Wiener processes of two types for edge OSS computing","authors":"Y. Tamura, S. Yamada","doi":"10.1080/15326349.2022.2149555","DOIUrl":"https://doi.org/10.1080/15326349.2022.2149555","url":null,"abstract":"","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44828675","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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