{"title":"The asymptotic normality for the least squares estimator of parameters in a two dimensional sinusoidal model of observations","authors":"O. Ivanov, O. Lymar","doi":"10.1090/tpms/1100","DOIUrl":"https://doi.org/10.1090/tpms/1100","url":null,"abstract":"","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2020-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42472095","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The wave equation in the three-dimensional space driven by a general stochastic measure","authors":"I. Bodnarchuk, V. Radchenko","doi":"10.1090/tpms/1097","DOIUrl":"https://doi.org/10.1090/tpms/1097","url":null,"abstract":"","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2020-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/tpms/1097","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48230621","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Editorial","authors":"","doi":"10.1090/tpms/1094","DOIUrl":"https://doi.org/10.1090/tpms/1094","url":null,"abstract":"","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2020-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43049641","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We provide the dual result of the Yamada–Watanabe theorem for mild solutions to semilinear stochastic partial differential equations with path-dependent coefficients. An essential tool is the so-called “method of the moving frame”, which allows us to reduce the proof to infinite dimensional stochastic differential equations.
{"title":"The dual Yamada–Watanabe theorem for mild solutions to stochastic partial differential equations","authors":"Stefan Tappe","doi":"10.1090/tpms/1155","DOIUrl":"https://doi.org/10.1090/tpms/1155","url":null,"abstract":"We provide the dual result of the Yamada–Watanabe theorem for mild solutions to semilinear stochastic partial differential equations with path-dependent coefficients. An essential tool is the so-called “method of the moving frame”, which allows us to reduce the proof to infinite dimensional stochastic differential equations.","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2020-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47066248","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Continuous time random walks (CTRWs) have random waiting times between particle jumps. Based on Ehrenfest-Brillouin-type model motivated by economics, we define the correlated CTRW that converge to the fractional Jacobi diffusion Y (E(t)), t ≥ 0, defined as a time change of Jacobi diffusion process Y (t) to the inverse E(t) of the standard stable subordinator. In the CTRW considered in this paper, the jumps are correlated so that in the limit the outer process Y (t) is not a L´evy process but a diffusion process with non-independent increments. The waiting times between jumps are selected from the domain of attraction of a stable law, so that the correlated CTRWs with these waiting times converge to Y (E(t)).
{"title":"Ehrenfest–Brillouin-type correlated continuous time random walk and fractional Jacobi diffusion","authors":"N. Leonenko, I. Papic, A. Sikorskii, N. Šuvak","doi":"10.1090/TPMS/1086","DOIUrl":"https://doi.org/10.1090/TPMS/1086","url":null,"abstract":"Continuous time random walks (CTRWs) have random waiting times between particle \u0000jumps. Based on Ehrenfest-Brillouin-type model motivated by economics, we define the correlated \u0000CTRW that converge to the fractional Jacobi diffusion Y (E(t)), t ≥ 0, defined as a time change of \u0000Jacobi diffusion process Y (t) to the inverse E(t) of the standard stable subordinator. In the CTRW \u0000considered in this paper, the jumps are correlated so that in the limit the outer process Y (t) is not \u0000a L´evy process but a diffusion process with non-independent increments. The waiting times between \u0000jumps are selected from the domain of attraction of a stable law, so that the correlated CTRWs with \u0000these waiting times converge to Y (E(t)).","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2020-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/TPMS/1086","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43316373","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
After the much too premature loss, earlier this year, of our greatly loved and admired colleague and co-editor of this journal, Prof. Ryuichi Kitamura, it was clear for the two of us that we would help to realize this tribute chosen by the editors—chosen to celebrate and honor his life and contribution to his field of study, but also and in particular his work for this journal. Ryuichi had been editor of Transportation since 1990, after earlier guestediting a special issue on ‘‘Activity-based Travel Analysis: a Retrospective Evaluation and Some Recent Contributions’’ with the late Eric Pas and Frank Koppelman. Since then he assisted and supported a large number of authors in publishing their papers to the standards of the journal, and with this helped to define the style of Transportation and to build its reputation. While his some 280 publications have appeared in many journals, it could be said that Transportation was his ‘‘home journal’’. It is therefore entirely fitting that this special issue will be devoted to reprising work from Ryuichi’s own hand—excellent research that originally appeared in reports or in conference proceedings, and thus may not have achieved the visibility it deserves. Because of our criteria that the work (1) should not have been published in the readily accessible peer-reviewed literature and (2) should not have been largely superseded by later developments, these selections do not pretend to constitute a fully representative cross-section of Ryuichi’s contributions. Nevertheless, they do offer a broad view of the variety of topics he addressed and the methodological approaches he brought to his research. They were chosen in part because we believe them still to be of current interest. Specifically, the six papers we selected address most of the key themes which engaged Ryuichi’s scientific curiosity and scholarship: the need for a dynamic, activity-based approach to analyzing travel behavior, the importance of values/attitudes, humans’ need to travel for its own sake (including seeing the automobile as an end in itself, as well as a
{"title":"Editorial","authors":"Patricia L. Mokhtarian, Kay W. Axhausen","doi":"10.1090/tpms/1093","DOIUrl":"https://doi.org/10.1090/tpms/1093","url":null,"abstract":"After the much too premature loss, earlier this year, of our greatly loved and admired colleague and co-editor of this journal, Prof. Ryuichi Kitamura, it was clear for the two of us that we would help to realize this tribute chosen by the editors—chosen to celebrate and honor his life and contribution to his field of study, but also and in particular his work for this journal. Ryuichi had been editor of Transportation since 1990, after earlier guestediting a special issue on ‘‘Activity-based Travel Analysis: a Retrospective Evaluation and Some Recent Contributions’’ with the late Eric Pas and Frank Koppelman. Since then he assisted and supported a large number of authors in publishing their papers to the standards of the journal, and with this helped to define the style of Transportation and to build its reputation. While his some 280 publications have appeared in many journals, it could be said that Transportation was his ‘‘home journal’’. It is therefore entirely fitting that this special issue will be devoted to reprising work from Ryuichi’s own hand—excellent research that originally appeared in reports or in conference proceedings, and thus may not have achieved the visibility it deserves. Because of our criteria that the work (1) should not have been published in the readily accessible peer-reviewed literature and (2) should not have been largely superseded by later developments, these selections do not pretend to constitute a fully representative cross-section of Ryuichi’s contributions. Nevertheless, they do offer a broad view of the variety of topics he addressed and the methodological approaches he brought to his research. They were chosen in part because we believe them still to be of current interest. Specifically, the six papers we selected address most of the key themes which engaged Ryuichi’s scientific curiosity and scholarship: the need for a dynamic, activity-based approach to analyzing travel behavior, the importance of values/attitudes, humans’ need to travel for its own sake (including seeing the automobile as an end in itself, as well as a","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2020-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43326191","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Minimax estimators of parameters of a regression model","authors":"A. Ivanov, I. Matsak","doi":"10.1090/tpms/1082","DOIUrl":"https://doi.org/10.1090/tpms/1082","url":null,"abstract":"","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2020-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48982963","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Orthogonal regression method for observations from a mixture","authors":"R. Maiboroda, G. Navara, O. Sugakova","doi":"10.1090/tpms/1088","DOIUrl":"https://doi.org/10.1090/tpms/1088","url":null,"abstract":"","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2020-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/tpms/1088","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41962528","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider a special class of weak dependent random variables with control on covariances of Lipschitz transformations. This class includes, but is not limited to, positively, negatively associated variables and a few other classes of weakly dependent structures. We prove the Strong Law of Large Numbers with the characterization of convergence rates which is almost optimal, in the sense that it is arbitrarily close to the optimal rate for independent variables. Moreover, we prove an inequality comparing the joint distributions with the product distributions of the margins, similar to the well known Newman’s inequality for characteristic functions of associated variables. As a consequence, we prove the Central Limit Theorem together with its functional counterpart, and also the convergence of the empirical process for this class of weak dependent variables.
{"title":"Asymptotic results for certain weak dependent variables","authors":"Idir Arab, P. E. Oliveira","doi":"10.1090/TPMS/1077","DOIUrl":"https://doi.org/10.1090/TPMS/1077","url":null,"abstract":"We consider a special class of weak dependent random variables with control on covariances of Lipschitz transformations. This class includes, but is not limited to, positively, negatively associated variables and a few other classes of weakly dependent structures. We prove the Strong Law of Large Numbers with the characterization of convergence rates which is almost optimal, in the sense that it is arbitrarily close to the optimal rate for independent variables. Moreover, we prove an inequality comparing the joint distributions with the product distributions of the margins, similar to the well known Newman’s inequality for characteristic functions of associated variables. As a consequence, we prove the Central Limit Theorem together with its functional counterpart, and also the convergence of the empirical process for this class of weak dependent variables.","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2020-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45987774","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Properties and distributions of values of fractal functions related to $boldsymbol {Q_2}$-representations of real numbers","authors":"M. Pratsiovytyi, S. Ratushniak","doi":"10.1090/tpms/1091","DOIUrl":"https://doi.org/10.1090/tpms/1091","url":null,"abstract":"","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2020-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43684386","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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