{"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":"99 1","pages":"169-188"},"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":"2 1","pages":"19-36"},"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":"99 1","pages":"211-228"},"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}
{"title":"Construction of the Karhunen–Loève model for an input Gaussian process in a linear system by using the output process","authors":"Yury V. Kozachenko, I. Rozora","doi":"10.1090/tpms/1084","DOIUrl":"https://doi.org/10.1090/tpms/1084","url":null,"abstract":"","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":"99 1","pages":"113-124"},"PeriodicalIF":0.9,"publicationDate":"2020-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/tpms/1084","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47022418","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":"On the lack of memory for distributions of overshoot functionals in the case of upper almost semicontinuous processes defined on a Markov chain","authors":"D. Gusak, E. V. Karnaukh","doi":"10.1090/tpms/1081","DOIUrl":"https://doi.org/10.1090/tpms/1081","url":null,"abstract":"","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":"99 1","pages":"77-89"},"PeriodicalIF":0.9,"publicationDate":"2020-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42165721","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":"Asymptotic distribution of the maximum likelihood estimator in the fractional Vašíček model","authors":"S. Lohvinenko, K. Ralchenko","doi":"10.1090/tpms/1087","DOIUrl":"https://doi.org/10.1090/tpms/1087","url":null,"abstract":"","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":"99 1","pages":"149-168"},"PeriodicalIF":0.9,"publicationDate":"2020-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48398889","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":"Approximation of solutions of the wave equation driven by a stochastic measure","authors":"V. Radchenko, N. Stefans’ka","doi":"10.1090/tpms/1092","DOIUrl":"https://doi.org/10.1090/tpms/1092","url":null,"abstract":"","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":"99 1","pages":"229-238"},"PeriodicalIF":0.9,"publicationDate":"2020-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/tpms/1092","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46484092","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":"Evaluation of extreme values of entropy functionals","authors":"Y. Mishura, H. Zhelezniak","doi":"10.1090/tpms/1090","DOIUrl":"https://doi.org/10.1090/tpms/1090","url":null,"abstract":"","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":"99 1","pages":"199-210"},"PeriodicalIF":0.9,"publicationDate":"2020-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41409522","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":"Calculation of the convexity adjustment to the forward rate in the Vasicek model for the forward in-arrears contracts on LIBOR rate","authors":"N. Malykh, I. S. Postevoy","doi":"10.1090/tpms/1089","DOIUrl":"https://doi.org/10.1090/tpms/1089","url":null,"abstract":"","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":"99 1","pages":"189-198"},"PeriodicalIF":0.9,"publicationDate":"2020-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44152152","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}
In this paper, the Stein-Haff identity is established for positive-definite and symmetric random matrices belonging to the exponential family. The identity is then applied to the matrix-variate gam ...
本文建立了指数族正定对称随机矩阵的Stein-Haff恒等式。然后将恒等式应用于矩阵变量博弈。
{"title":"Stein–Haff identity for the exponential family","authors":"Gustav Alfelt","doi":"10.1090/TPMS/1076","DOIUrl":"https://doi.org/10.1090/TPMS/1076","url":null,"abstract":"In this paper, the Stein-Haff identity is established for positive-definite and symmetric random matrices belonging to the exponential family. The identity is then applied to the matrix-variate gam ...","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":"99 1","pages":"5-17"},"PeriodicalIF":0.9,"publicationDate":"2020-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44960344","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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