Pub Date : 2023-11-01DOI: 10.1137/s0040585x97t991593
I. Karatzas, W. Schachermayer
{"title":"A Weak Law of Large Numbers for Dependent Random Variables","authors":"I. Karatzas, W. Schachermayer","doi":"10.1137/s0040585x97t991593","DOIUrl":"https://doi.org/10.1137/s0040585x97t991593","url":null,"abstract":"","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135510179","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 : 2023-11-01DOI: 10.1137/s0040585x97t991519
A. A. Borovkov
Under the assumption that the change-point time is large, a Poisson approximation for the distribution of the number of false alarms is obtained. We also find upper bounds for the probability of a ``false alarm” on a given time interval. An asymptotic expansion for the mean delay time of the alarm signal relative to the change-point time is obtained. To get this result, we establish the exponential convergence rate in the ergodic theorem for Markov chains with a positive atom; chains of this kind describe the monitoring of control systems. A game-theoretic approach is employed to obtain asymptotically optimal solutions of the change-point problem.
{"title":"On the Asymptotic Approach to the Change-Point Problem and Exponential Convergence Rate in the Ergodic Theorem for Markov Chains","authors":"A. A. Borovkov","doi":"10.1137/s0040585x97t991519","DOIUrl":"https://doi.org/10.1137/s0040585x97t991519","url":null,"abstract":"Under the assumption that the change-point time is large, a Poisson approximation for the distribution of the number of false alarms is obtained. We also find upper bounds for the probability of a ``false alarm” on a given time interval. An asymptotic expansion for the mean delay time of the alarm signal relative to the change-point time is obtained. To get this result, we establish the exponential convergence rate in the ergodic theorem for Markov chains with a positive atom; chains of this kind describe the monitoring of control systems. A game-theoretic approach is employed to obtain asymptotically optimal solutions of the change-point problem.","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135515944","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 : 2023-11-01DOI: 10.1137/s0040585x97t991532
V. A. Vatutin, E. E. Dyakonova
{"title":"Population Size of a Critical Branching Process Evolving in an Unfavorable Environment","authors":"V. A. Vatutin, E. E. Dyakonova","doi":"10.1137/s0040585x97t991532","DOIUrl":"https://doi.org/10.1137/s0040585x97t991532","url":null,"abstract":"","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135510181","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 : 2023-11-01DOI: 10.1137/s0040585x97t991520
A. V. Bulinski
It is shown that widely used suboptimal algorithms of feature selection based on information theory concepts do not necessarily identify a collection of features (relevant in a sense) affecting the studied random response. This can be considered as a reflection of the epistasis phenomenon known in genetics, when individual features have little effect on increased risk of complex disease, whereas certain combinations of features have significant impact on risk. It is demonstrated that a similar effect is also manifested in inferences employing statistical estimates of mutual information.
{"title":"On Relevant Features Selection Based on Information Theory","authors":"A. V. Bulinski","doi":"10.1137/s0040585x97t991520","DOIUrl":"https://doi.org/10.1137/s0040585x97t991520","url":null,"abstract":"It is shown that widely used suboptimal algorithms of feature selection based on information theory concepts do not necessarily identify a collection of features (relevant in a sense) affecting the studied random response. This can be considered as a reflection of the epistasis phenomenon known in genetics, when individual features have little effect on increased risk of complex disease, whereas certain combinations of features have significant impact on risk. It is demonstrated that a similar effect is also manifested in inferences employing statistical estimates of mutual information.","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135515946","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 : 2023-11-01DOI: 10.1137/s0040585x97t991544
A. M. Vershik, M. A. Lifshits
{"title":"On mm-Entropy of a Banach Space with Gaussian Measure","authors":"A. M. Vershik, M. A. Lifshits","doi":"10.1137/s0040585x97t991544","DOIUrl":"https://doi.org/10.1137/s0040585x97t991544","url":null,"abstract":"","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135515943","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 : 2023-11-01DOI: 10.1137/s0040585x97t99160x
N. V. Krylov
{"title":"On Nondegenerate Itô Processes with Moderated Drift","authors":"N. V. Krylov","doi":"10.1137/s0040585x97t99160x","DOIUrl":"https://doi.org/10.1137/s0040585x97t99160x","url":null,"abstract":"","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135510185","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 : 2023-11-01DOI: 10.1137/s0040585x97t991490
A. N. Shiryaev
{"title":"On the 120th Birthday of Andrei Nikolaevich Kolmogorov","authors":"A. N. Shiryaev","doi":"10.1137/s0040585x97t991490","DOIUrl":"https://doi.org/10.1137/s0040585x97t991490","url":null,"abstract":"","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135515945","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 : 2023-08-01DOI: 10.1137/s0040585x97t991453
M. Skorski
The statistical inference on missing mass aims to estimate the weight of elements not observed during sampling. Since the pioneer work of Good and Turing, the problem has been studied in many areas, including statistical linguistics, ecology, and machine learning. Proving the sub-Gaussian behavior of the missing mass has been notoriously hard, and a number of complicated arguments have been proposed: logarithmic Sobolev inequalities, thermodynamic approaches, and information-theoretic transportation methods. Prior works have argued that the difficulty is inherent, and classical tools are inadequate. We show that this common belief is false, and all that we need to establish the sub-Gaussian concentration is the classical inequality of Bernstein. The strong educational value of our work is in its demonstration of this inequality in its full generality, an aspect not well recognized by researchers.
{"title":"On Sub-Gaussian Concentration of Missing Mass","authors":"M. Skorski","doi":"10.1137/s0040585x97t991453","DOIUrl":"https://doi.org/10.1137/s0040585x97t991453","url":null,"abstract":"The statistical inference on missing mass aims to estimate the weight of elements not observed during sampling. Since the pioneer work of Good and Turing, the problem has been studied in many areas, including statistical linguistics, ecology, and machine learning. Proving the sub-Gaussian behavior of the missing mass has been notoriously hard, and a number of complicated arguments have been proposed: logarithmic Sobolev inequalities, thermodynamic approaches, and information-theoretic transportation methods. Prior works have argued that the difficulty is inherent, and classical tools are inadequate. We show that this common belief is false, and all that we need to establish the sub-Gaussian concentration is the classical inequality of Bernstein. The strong educational value of our work is in its demonstration of this inequality in its full generality, an aspect not well recognized by researchers.","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136021783","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 : 2023-08-01DOI: 10.1137/s0040585x97t991489
K. Yu. Klimov, M. N. Tsareva
This note presents information about three workshops on financial and actuarial mathematics held in 2022 by The Vega Institute Science Promotion Foundation. The goal of the Foundation is to support and develop projects for training highly qualified personnel in the field of financial and actuarial mathematics in parallel with its economic and numerical components.
{"title":"On Student Workshops Organized by the Vega Institute","authors":"K. Yu. Klimov, M. N. Tsareva","doi":"10.1137/s0040585x97t991489","DOIUrl":"https://doi.org/10.1137/s0040585x97t991489","url":null,"abstract":"This note presents information about three workshops on financial and actuarial mathematics held in 2022 by The Vega Institute Science Promotion Foundation. The goal of the Foundation is to support and develop projects for training highly qualified personnel in the field of financial and actuarial mathematics in parallel with its economic and numerical components.","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136021780","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 : 2023-08-01DOI: 10.1137/s0040585x97t991416
M. M. Xi, X. Q. Li, L. Chen, X. J. Wang
We study complete and complete integration convergence for arrays of rowwise extended negatively dependent random variables under sublinear expectations. Our results generalize complete moment convergence results of [T.-C. Hu, K.-L. Wang, and A. Rosalsky, Sankhya A, 77 (2015), pp. 1--29] and [Y. Wu, M. Ordón͂ez Cabrera, and A. Volodin, Glas. Mat. Ser. III, 49(69) (2014), pp. 447--466] from classical probability spaces to spaces with sublinear expectation.
研究了次线性期望下行扩展负相关随机变量阵列的完全收敛性和完全收敛性。我们的结果推广了[t . c .]的完全矩收敛结果。胡,K.-L。Wang, A. Rosalsky, Sankhya A, 77 (2015)， pp 1—29。Wu, M. Ordón ez Cabrera，和A. Volodin, glass。垫,爵士。III, 49(69) (2014)， pp. 447—466]从经典概率空间到次线性期望空间。
{"title":"Complete and Complete Integral Convergence for Arrays of Rowwise Extended Negatively Dependent Random Variables under Sublinear Expectations","authors":"M. M. Xi, X. Q. Li, L. Chen, X. J. Wang","doi":"10.1137/s0040585x97t991416","DOIUrl":"https://doi.org/10.1137/s0040585x97t991416","url":null,"abstract":"We study complete and complete integration convergence for arrays of rowwise extended negatively dependent random variables under sublinear expectations. Our results generalize complete moment convergence results of [T.-C. Hu, K.-L. Wang, and A. Rosalsky, Sankhya A, 77 (2015), pp. 1--29] and [Y. Wu, M. Ordón͂ez Cabrera, and A. Volodin, Glas. Mat. Ser. III, 49(69) (2014), pp. 447--466] from classical probability spaces to spaces with sublinear expectation.","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136021782","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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