Pub Date : 2022-11-21DOI: 10.1080/15326349.2022.2144377
V. Kulkarni, Li Xiao, Hanqin Zhang
Abstract We consider a periodic review inventory system with multiclass demands and fixed setup cost. Demand arrivals of each class are assumed to be a Poisson process, and a lost-sales setting is adopted. The demand classes are classified by the cost of their unsatisfied demands. We consider two cases: the leftover inventory at the end of a restocking interval is entirely discarded or entirely carried over to the next period. We obtain the optimal rationing policy, the optimal ordering policy and the optimal duration of the periodic review interval that minimize the average cost per unit time. We derive the differential equations satisfied by the value function characterized by the on-hand inventory level and the residual restocking time. This value function does not have the traditional modularity and convexity properties. Hence, the optimal policy is derived directly based on the ordinary differential equations satisfied by the value function. Moreover, some structural properties of the optimal policy such as the monotone property of the optimal rationing policy are obtained.
{"title":"Periodic review inventory models with multiclass demands and fixed order costs","authors":"V. Kulkarni, Li Xiao, Hanqin Zhang","doi":"10.1080/15326349.2022.2144377","DOIUrl":"https://doi.org/10.1080/15326349.2022.2144377","url":null,"abstract":"Abstract We consider a periodic review inventory system with multiclass demands and fixed setup cost. Demand arrivals of each class are assumed to be a Poisson process, and a lost-sales setting is adopted. The demand classes are classified by the cost of their unsatisfied demands. We consider two cases: the leftover inventory at the end of a restocking interval is entirely discarded or entirely carried over to the next period. We obtain the optimal rationing policy, the optimal ordering policy and the optimal duration of the periodic review interval that minimize the average cost per unit time. We derive the differential equations satisfied by the value function characterized by the on-hand inventory level and the residual restocking time. This value function does not have the traditional modularity and convexity properties. Hence, the optimal policy is derived directly based on the ordinary differential equations satisfied by the value function. Moreover, some structural properties of the optimal policy such as the monotone property of the optimal rationing policy are obtained.","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44068880","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 : 2022-11-18DOI: 10.1080/15326349.2022.2134896
T. Bielecki, J. Jakubowski, Mariusz Niewęgłowski
Abstract This work contributes to the theory of Hawkes processes. We introduce and study a new class of Hawkes processes that we call generalized Hawkes processes, and their special subclass – the generalized multivariate Hawkes processes (GMHPs). GMHPs are multivariate marked point processes that add an important feature to the family of the (classical) multivariate Hawkes processes: they allow for explicit modeling of simultaneous occurrence of excitation events coming from different sources, i.e., caused by different coordinates of the multivariate process.
{"title":"Multivariate Hawkes processes with simultaneous occurrence of excitation events coming from different sources","authors":"T. Bielecki, J. Jakubowski, Mariusz Niewęgłowski","doi":"10.1080/15326349.2022.2134896","DOIUrl":"https://doi.org/10.1080/15326349.2022.2134896","url":null,"abstract":"Abstract This work contributes to the theory of Hawkes processes. We introduce and study a new class of Hawkes processes that we call generalized Hawkes processes, and their special subclass – the generalized multivariate Hawkes processes (GMHPs). GMHPs are multivariate marked point processes that add an important feature to the family of the (classical) multivariate Hawkes processes: they allow for explicit modeling of simultaneous occurrence of excitation events coming from different sources, i.e., caused by different coordinates of the multivariate process.","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47880570","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 : 2022-11-07DOI: 10.1080/15326349.2022.2139271
M. González, M. Molina, I. D. del Puerto
The 5th International Workshop on Branching Processes and their Applications (IWBPA2021) was held on 6th, 8th, 13th, 15th, 20th and 22nd April 2021. It was the last in a series of meetings held every three years in Badajoz (Spain). Due to the COVID-19 pandemic, the IWBPA2021 took place virtually using video conferencing tools. The 2021 year’s conference continued the tradition of the previous meetings in facilitating the exchange of research ideas in this field and related processes. The IWBPA2021 meeting was the fifth in the series of IWBPAs promoted and organized since 2009 by the research group Branching Processes and their Applications at the Department of Mathematics of the University of Extremadura, Spain, and scientifically sponsored by the Spanish Society for Statistics and Operations Research (Sociedad de Estad ıstica e Investigaci on Operativa) and the Institute of Advanced Scientific Computation of Extremadura (Instituto de Computaci on Cient ıfica Avanzada de Extremadura). There were 145 participants and 58 speakers from 22 countries who contributed to the success of the workshop. The presentations at the workshop maintained a healthy balance between the theoretical and practical aspects of branching processes. The speakers articulated the fact that this research area is very active and produces interesting results. The conference program and talks are available on the website (https://sites.google.com/view/iwbpa21-branching-unex). The Proceedings consist of 15 selected papers whose topics have been classified into the following parts:
第五届分支过程及其应用国际研讨会（IWBPA2021）于2021年4月6日、8日、13日、15日、20日和22日举行。这是每三年在巴达霍斯（西班牙）举行的一系列会议中的最后一次。由于新冠肺炎大流行，IWBPA2021实际上是使用视频会议工具举行的。2021年的会议延续了以往会议的传统，促进了该领域和相关过程的研究思想交流。IWBPA2021会议是西班牙埃斯特雷马杜拉大学数学系分支过程及其应用研究小组自2009年以来推动和组织的一系列IWBPA中的第五次会议，由西班牙统计与运筹学学会（Sociedad de Estadıstica e Investigaci on Operativa）和埃斯特雷马杜拉高级科学计算研究所（Instituto de Computaci on Cientıfica Avanzada de Extremedura）科学赞助。来自22个国家的145名与会者和58名发言者为研讨会的成功做出了贡献。研讨会上的演讲在分支过程的理论和实践方面保持了健康的平衡。发言者阐述了这样一个事实，即这一研究领域非常活跃，产生了有趣的结果。会议计划和会谈可在网站上查看(https://sites.google.com/view/iwbpa21-branching-unex)。论文集由15篇精选论文组成，其主题分为以下部分：
{"title":"Preface of the special issue on Branching Processes and Applications (IWBPA2021)","authors":"M. González, M. Molina, I. D. del Puerto","doi":"10.1080/15326349.2022.2139271","DOIUrl":"https://doi.org/10.1080/15326349.2022.2139271","url":null,"abstract":"The 5th International Workshop on Branching Processes and their Applications (IWBPA2021) was held on 6th, 8th, 13th, 15th, 20th and 22nd April 2021. It was the last in a series of meetings held every three years in Badajoz (Spain). Due to the COVID-19 pandemic, the IWBPA2021 took place virtually using video conferencing tools. The 2021 year’s conference continued the tradition of the previous meetings in facilitating the exchange of research ideas in this field and related processes. The IWBPA2021 meeting was the fifth in the series of IWBPAs promoted and organized since 2009 by the research group Branching Processes and their Applications at the Department of Mathematics of the University of Extremadura, Spain, and scientifically sponsored by the Spanish Society for Statistics and Operations Research (Sociedad de Estad ıstica e Investigaci on Operativa) and the Institute of Advanced Scientific Computation of Extremadura (Instituto de Computaci on Cient ıfica Avanzada de Extremadura). There were 145 participants and 58 speakers from 22 countries who contributed to the success of the workshop. The presentations at the workshop maintained a healthy balance between the theoretical and practical aspects of branching processes. The speakers articulated the fact that this research area is very active and produces interesting results. The conference program and talks are available on the website (https://sites.google.com/view/iwbpa21-branching-unex). The Proceedings consist of 15 selected papers whose topics have been classified into the following parts:","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45036407","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 : 2022-09-16DOI: 10.1080/15326349.2022.2112604
Fen Jiang, Miaomiao Wang, Xuejun Wang
Abstract In this article, we prove the complete q-th moment convergence for the maximum of partial sums of -negatively associated random variables under some general conditions. The results obtained in this article are extensions of previous studies for -negatively associated random variables. In addition, we investigate the strong consistency of the least squares estimator in the simple linear errors-in-variables model based on -negatively associated random variables, and provide some simulations to assess the finite sample performance of the theoretical results.
{"title":"Complete q-th moment convergence for the maximum of partial sums of -negatively associated random variables and its application to the EV regression model*","authors":"Fen Jiang, Miaomiao Wang, Xuejun Wang","doi":"10.1080/15326349.2022.2112604","DOIUrl":"https://doi.org/10.1080/15326349.2022.2112604","url":null,"abstract":"Abstract In this article, we prove the complete q-th moment convergence for the maximum of partial sums of -negatively associated random variables under some general conditions. The results obtained in this article are extensions of previous studies for -negatively associated random variables. In addition, we investigate the strong consistency of the least squares estimator in the simple linear errors-in-variables model based on -negatively associated random variables, and provide some simulations to assess the finite sample performance of the theoretical results.","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47145089","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 : 2022-09-15DOI: 10.1080/15326349.2022.2114496
R. Butler
Abstract Asymptotic residue expansions are proposed for inverting probability generating functions (PGFs) and approximating their associated mass and survival functions. The expansions are useful in the wide range of stochastic model applications in which a PGF admits poles in its analytic continuation. The error of such an expansion is a contour integral in the analytic continuation and saddlepoint approximations are developed for such errors using the method of steepest descents. These saddlepoint error estimates attain sufficient accuracy that they can be used to set the order of the expansion so it achieves a specified error. Numerical applications include a success run tutorial example, the discrete ruin model, the Pollaczek-Khintchine formula, and passage times for semi-Markov processes. The residue expansions apply more generally for inverting generating functions which arise in renewal theory and combinatorics and lead to a simple proof of the classic renewal theorem. They extend even further for determining Taylor coefficients of general meromorphic functions.
{"title":"Residue expansions and saddlepoint approximations in stochastic models using the analytic continuation of generating functions","authors":"R. Butler","doi":"10.1080/15326349.2022.2114496","DOIUrl":"https://doi.org/10.1080/15326349.2022.2114496","url":null,"abstract":"Abstract Asymptotic residue expansions are proposed for inverting probability generating functions (PGFs) and approximating their associated mass and survival functions. The expansions are useful in the wide range of stochastic model applications in which a PGF admits poles in its analytic continuation. The error of such an expansion is a contour integral in the analytic continuation and saddlepoint approximations are developed for such errors using the method of steepest descents. These saddlepoint error estimates attain sufficient accuracy that they can be used to set the order of the expansion so it achieves a specified error. Numerical applications include a success run tutorial example, the discrete ruin model, the Pollaczek-Khintchine formula, and passage times for semi-Markov processes. The residue expansions apply more generally for inverting generating functions which arise in renewal theory and combinatorics and lead to a simple proof of the classic renewal theorem. They extend even further for determining Taylor coefficients of general meromorphic functions.","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47225723","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 : 2022-09-10DOI: 10.1080/15326349.2022.2117195
Junjun Zheng, H. Okamura, T. Dohi
{"title":"Sensitivity analysis for a Markov regenerative software rejuvenation model","authors":"Junjun Zheng, H. Okamura, T. Dohi","doi":"10.1080/15326349.2022.2117195","DOIUrl":"https://doi.org/10.1080/15326349.2022.2117195","url":null,"abstract":"","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43935327","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 : 2022-08-27DOI: 10.1080/15326349.2022.2112225
Bora Çekyay, S. Özekici
Abstract We analyze mean time to failure and availability of systems that perform semi-Markov missions. The mission process is the minimal semi-Markov process associated with a Markov renewal process. Therefore, the successive phases of the mission follow a Markov chain, and the phase durations are generally distributed. The lifetimes of the non-identical components in the system are assumed to be generally distributed and are modeled using intrinsic aging concepts. Moreover, the lifetime parameters of the components and the configuration of the system change depending on the phases of the mission. We characterize the mean time to failure through solving a Poisson equation, and we analyze the system availability assuming that repair duration has a general distribution which is dependent on the phase of the mission during which the failure has occurred and on the deterioration level of the system.
{"title":"MTTF and availability of semi-Markov missions with non-identical generally distributed component lifetimes","authors":"Bora Çekyay, S. Özekici","doi":"10.1080/15326349.2022.2112225","DOIUrl":"https://doi.org/10.1080/15326349.2022.2112225","url":null,"abstract":"Abstract We analyze mean time to failure and availability of systems that perform semi-Markov missions. The mission process is the minimal semi-Markov process associated with a Markov renewal process. Therefore, the successive phases of the mission follow a Markov chain, and the phase durations are generally distributed. The lifetimes of the non-identical components in the system are assumed to be generally distributed and are modeled using intrinsic aging concepts. Moreover, the lifetime parameters of the components and the configuration of the system change depending on the phases of the mission. We characterize the mean time to failure through solving a Poisson equation, and we analyze the system availability assuming that repair duration has a general distribution which is dependent on the phase of the mission during which the failure has occurred and on the deterioration level of the system.","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46798700","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 : 2022-08-22DOI: 10.1080/15326349.2022.2107666
S. Kayal, Raju Bhakta, N. Balakrishnan
Abstract Finite mixture (FM) models have found key applications in many fields. Recently, some discussions have been made on comparing finite mixture models. In this paper, we discuss stochastic comparison of two FM models with respect to usual stochastic order when the mixture components have a general family of distributions. This problem has been studied when there is heterogeneity in one parameter (i.e., the distributional parameter), as well as when there is heterogeneity in two parameters (i.e., the distributional parameter and the mixing proportions). The sufficient conditions considered are based on p-larger order and reciprocally majorization order. Several examples have been provided to illustrate the established results.
{"title":"Some results on stochastic comparisons of two finite mixture models with general components","authors":"S. Kayal, Raju Bhakta, N. Balakrishnan","doi":"10.1080/15326349.2022.2107666","DOIUrl":"https://doi.org/10.1080/15326349.2022.2107666","url":null,"abstract":"Abstract Finite mixture (FM) models have found key applications in many fields. Recently, some discussions have been made on comparing finite mixture models. In this paper, we discuss stochastic comparison of two FM models with respect to usual stochastic order when the mixture components have a general family of distributions. This problem has been studied when there is heterogeneity in one parameter (i.e., the distributional parameter), as well as when there is heterogeneity in two parameters (i.e., the distributional parameter and the mixing proportions). The sufficient conditions considered are based on p-larger order and reciprocally majorization order. Several examples have been provided to illustrate the established results.","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48858509","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 : 2022-08-19DOI: 10.1080/15326349.2022.2108452
V. Ejov, J. Filar, Zhihao Qiao
Abstract We consider the problem of parametric sensitivity of a particular characterization of risk, with respect to a threshold parameter Such threshold risk is modeled as the probability of a perturbed function of a random variable falling below 0. We demonstrate that for polynomial and rational functions of that random variable there exist at most finitely many risk critical points. The latter are those special values of the threshold parameter for which rate of change of risk is unbounded as δ approaches them. Under weak conditions, we characterize candidates for risk critical points as zeroes of either the discriminant of a relevant perturbed polynomial, or of its leading coefficient, or both. Thus the equations that need to be solved are themselves polynomial equations in δ that exploit the algebraic properties of the underlying polynomial or rational functions. We name these important equations as” hidden equations of risk critical thresholds”.
{"title":"Hidden equations of risk critical thresholds","authors":"V. Ejov, J. Filar, Zhihao Qiao","doi":"10.1080/15326349.2022.2108452","DOIUrl":"https://doi.org/10.1080/15326349.2022.2108452","url":null,"abstract":"Abstract We consider the problem of parametric sensitivity of a particular characterization of risk, with respect to a threshold parameter Such threshold risk is modeled as the probability of a perturbed function of a random variable falling below 0. We demonstrate that for polynomial and rational functions of that random variable there exist at most finitely many risk critical points. The latter are those special values of the threshold parameter for which rate of change of risk is unbounded as δ approaches them. Under weak conditions, we characterize candidates for risk critical points as zeroes of either the discriminant of a relevant perturbed polynomial, or of its leading coefficient, or both. Thus the equations that need to be solved are themselves polynomial equations in δ that exploit the algebraic properties of the underlying polynomial or rational functions. We name these important equations as” hidden equations of risk critical thresholds”.","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48254482","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 : 2022-08-15DOI: 10.1080/15326349.2022.2100423
Jörn Sass, Dorothee Westphal, R. Wunderlich
Abstract In this paper we study a financial market in which stock returns depend on an unobservable Gaussian drift process. Investors obtain information on that drift from return observations and discrete-time expert opinions as an external source of information. Estimates of the hidden drift process are based on filtering techniques. Our focus is the case of high-frequency experts periodically providing their views on the drift with variances growing linearly with the arrival frequency. The latter condition guarantees that the delivered information per time is limited. The asymptotic behavior of the filter as the arrival frequency tends to infinity is described by limit theorems. These state that the information obtained from observing the discrete-time expert opinions is asymptotically the same as that from observing a certain diffusion process. We apply these diffusion approximations of the filter for deriving simplified approximate solutions of utility maximization problems with logarithmic and power utility.
{"title":"Diffusion approximations for periodically arriving expert opinions in a financial market with Gaussian drift","authors":"Jörn Sass, Dorothee Westphal, R. Wunderlich","doi":"10.1080/15326349.2022.2100423","DOIUrl":"https://doi.org/10.1080/15326349.2022.2100423","url":null,"abstract":"Abstract In this paper we study a financial market in which stock returns depend on an unobservable Gaussian drift process. Investors obtain information on that drift from return observations and discrete-time expert opinions as an external source of information. Estimates of the hidden drift process are based on filtering techniques. Our focus is the case of high-frequency experts periodically providing their views on the drift with variances growing linearly with the arrival frequency. The latter condition guarantees that the delivered information per time is limited. The asymptotic behavior of the filter as the arrival frequency tends to infinity is described by limit theorems. These state that the information obtained from observing the discrete-time expert opinions is asymptotically the same as that from observing a certain diffusion process. We apply these diffusion approximations of the filter for deriving simplified approximate solutions of utility maximization problems with logarithmic and power utility.","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46582844","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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