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Theory of Probability and its Applications最新文献

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On a Periodic Branching Random Walk on $mathbf{Z}^{{d}}$ with an Infinite Variance of Jumps 论$mathbf{Z}^{{d}}$上具有无限跳跃方差的周期性分支随机漫步
IF 0.6 4区 数学
Theory of Probability and its Applications Pub Date : 2024-05-02 DOI: 10.1137/s0040585x97t991763
K. S. Ryadovkin
{"title":"On a Periodic Branching Random Walk on $mathbf{Z}^{{d}}$ with an Infinite Variance of Jumps","authors":"K. S. Ryadovkin","doi":"10.1137/s0040585x97t991763","DOIUrl":"https://doi.org/10.1137/s0040585x97t991763","url":null,"abstract":"Theory of Probability &amp;Its Applications, Volume 69, Issue 1, Page 88-98, May 2024. <br/> We consider periodic branching random walks with periodic branching sources. It is assumed that the transition intensities of the random walk satisfy some symmetry conditions and obey a condition which ensures infinite variance of jumps. In this case, we obtain the leading term for the asymptotics of the mean population size of particles at an arbitrary point of the lattice for large time.","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140839311","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}
引用次数: 0
Hellinger Distance Estimation for Nonregular Spectra 非规则频谱的海灵格距离估计
IF 0.6 4区 数学
Theory of Probability and its Applications Pub Date : 2024-05-02 DOI: 10.1137/s0040585x97t991805
M. Taniguchi, Y. Xue
{"title":"Hellinger Distance Estimation for Nonregular Spectra","authors":"M. Taniguchi, Y. Xue","doi":"10.1137/s0040585x97t991805","DOIUrl":"https://doi.org/10.1137/s0040585x97t991805","url":null,"abstract":"Theory of Probability &amp;Its Applications, Volume 69, Issue 1, Page 150-160, May 2024. <br/> For Gaussian stationary processes, a time series Hellinger distance $T(f,g)$ for spectra $f$ and $g$ is derived. Evaluating $T(f_theta,f_{theta+h})$ of the form $O(h^alpha)$, we give $1/alpha$-consistent asymptotics of the maximum likelihood estimator of $theta$ for nonregular spectra. For regular spectra, we introduce the minimum Hellinger distance estimator $widehat{theta}=operatorname{arg}min_theta T(f_theta,widehat{g}_n)$, where $widehat{g}_n$ is a nonparametric spectral density estimator. We show that $widehattheta$ is asymptotically efficient and more robust than the Whittle estimator. Brief numerical studies are provided.","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140839537","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}
引用次数: 0
Stability Properties of Feature Selection Measures 特征选择措施的稳定性能
IF 0.6 4区 数学
Theory of Probability and its Applications Pub Date : 2024-05-02 DOI: 10.1137/s0040585x97t991726
A. V. Bulinski
{"title":"Stability Properties of Feature Selection Measures","authors":"A. V. Bulinski","doi":"10.1137/s0040585x97t991726","DOIUrl":"https://doi.org/10.1137/s0040585x97t991726","url":null,"abstract":"Theory of Probability &amp;Its Applications, Volume 69, Issue 1, Page 25-34, May 2024. <br/> In this paper, we prove that the monotonicity property of the stability measure for the feature (factor) selection introduced by Nogueira, Sechidis, and Brown [J. Mach. Learn. Res., 18 (2018), pp. 1--54] may not hold. Another monotonicity property takes place. We also show the cases in which it is possible to compare by certain parameters the matrices describing the operation of algorithms for identifying relevant features.","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140839614","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}
引用次数: 0
In Memory of V. N. Tutubalin (10.15.1936--6.18.2023) 纪念瓦-尼-图图巴林（1936 年 10 月 15 日--2023 年 6 月 18 日）
IF 0.6 4区 数学
Theory of Probability and its Applications Pub Date : 2024-05-02 DOI: 10.1137/s0040585x97t991829
S.A. Molchanov, D.D. Sokolov, E.B. Yarovaya
{"title":"In Memory of V. N. Tutubalin (10.15.1936--6.18.2023)","authors":"S.A. Molchanov, D.D. Sokolov, E.B. Yarovaya","doi":"10.1137/s0040585x97t991829","DOIUrl":"https://doi.org/10.1137/s0040585x97t991829","url":null,"abstract":"Theory of Probability &amp;Its Applications, Volume 69, Issue 1, Page 166-167, May 2024. <br/> A remembrance of Professor Valerii Nikolaevich Tutubalin, who passed away on June 18, 2023. He held a position in the Department of Probability Theory at Moscow State University since 1965 and was known as a leading authority on probability theory and its applications.","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140839355","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}
引用次数: 0
Markov Branching Random Walks on $mathbf{Z}_+$: An Approach Using Orthogonal Polynomials. I $mathbf{Z}_+$上的马尔科夫分支随机漫步：使用正交多项式的方法I
IF 0.6 4区 数学
Theory of Probability and its Applications Pub Date : 2024-05-02 DOI: 10.1137/s0040585x97t991751
A. V. Lyulintsev
{"title":"Markov Branching Random Walks on $mathbf{Z}_+$: An Approach Using Orthogonal Polynomials. I","authors":"A. V. Lyulintsev","doi":"10.1137/s0040585x97t991751","DOIUrl":"https://doi.org/10.1137/s0040585x97t991751","url":null,"abstract":"Theory of Probability &amp;Its Applications, Volume 69, Issue 1, Page 71-87, May 2024. <br/> We consider a continuous-time homogeneous Markov process on the state space $mathbf{Z}_+={0,1,2,dots}$. The process is interpreted as the motion of a particle. A particle may transit only to neighboring points $mathbf{Z}_+$, i.e., for each single motion of the particle, its coordinate changes by 1. The process is equipped with a branching mechanism. Branching sources may be located at each point of $mathbf{Z}_+$. At a moment of branching, new particles appear at the branching point and then evolve independently of each other (and of the other particles) by the same rules as the initial particle. To such a branching Markov process there corresponds a Jacobi matrix. In terms of orthogonal polynomials corresponding to this matrix, we obtain formulas for the mean number of particles at an arbitrary fixed point of $mathbf{Z}_+$ at time $t&gt;0$. The results obtained are applied to some concrete models, an exact value for the mean number of particles in terms of special functions is given, and an asymptotic formula for this quantity for large time is found.","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140839539","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}
引用次数: 0
Laplace Expansion for Bartlett--Nanda--Pillai Test Statistic and Its Error Bound 巴特利特-南达-皮莱检验统计量的拉普拉斯展开及其误差范围
IF 0.6 4区 数学
Theory of Probability and its Applications Pub Date : 2024-02-07 DOI: 10.1137/s0040585x97t991635
H. Wakaki, V. V. Ulyanov
{"title":"Laplace Expansion for Bartlett--Nanda--Pillai Test Statistic and Its Error Bound","authors":"H. Wakaki, V. V. Ulyanov","doi":"10.1137/s0040585x97t991635","DOIUrl":"https://doi.org/10.1137/s0040585x97t991635","url":null,"abstract":"Theory of Probability &amp;Its Applications, Volume 68, Issue 4, Page 570-581, February 2024. <br/> We construct asymptotic expansions for the distribution function of the Bartlett--Nanda--Pillai statistic under the condition that the null linear hypothesis is valid in a multivariate linear model. Computable estimates of the accuracy of approximation are obtained via the Laplace approximation method, which is generalized to integrals for matrix-valued functions.","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139769434","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}
引用次数: 0
On a Diffusion Approximation of a Prediction Game 论预测博弈的扩散近似法
IF 0.6 4区 数学
Theory of Probability and its Applications Pub Date : 2024-02-07 DOI: 10.1137/s0040585x97t991659
M. V. Zhitlukhin
{"title":"On a Diffusion Approximation of a Prediction Game","authors":"M. V. Zhitlukhin","doi":"10.1137/s0040585x97t991659","DOIUrl":"https://doi.org/10.1137/s0040585x97t991659","url":null,"abstract":"Theory of Probability &amp;Its Applications, Volume 68, Issue 4, Page 607-621, February 2024. <br/> This paper is concerned with a dynamic game-theoretic model, where the players place bets on outcomes of random events or random vectors. Our purpose here is to construct a diffusion approximation of the model in the case where all players follow nearly optimal strategies. This approximation is further used to study the limit dynamics of the model.","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139770954","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}
引用次数: 0
On Sufficient Conditions in the Marchenko--Pastur Theorem 论马琴科--帕斯图尔定理中的充分条件
IF 0.6 4区 数学
Theory of Probability and its Applications Pub Date : 2024-02-07 DOI: 10.1137/s0040585x97t991696
P. A. Yaskov
{"title":"On Sufficient Conditions in the Marchenko--Pastur Theorem","authors":"P. A. Yaskov","doi":"10.1137/s0040585x97t991696","DOIUrl":"https://doi.org/10.1137/s0040585x97t991696","url":null,"abstract":"Theory of Probability &amp;Its Applications, Volume 68, Issue 4, Page 657-673, February 2024. <br/> We find general sufficient conditions in the Marchenko--Pastur theorem for high-dimensional sample covariance matrices associated with random vectors, for which the weak concentration property of quadratic forms may not hold in general. The results are obtained by means of a new martingale method, which may be useful in other problems of random matrix theory.","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139770969","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}
引用次数: 0
On Forward and Backward Kolmogorov Equations for Pure Jump Markov Processes and Their Generalizations 论纯跃迁马尔可夫过程的前向和后向科尔莫哥洛夫方程及其泛化
IF 0.6 4区 数学
Theory of Probability and its Applications Pub Date : 2024-02-07 DOI: 10.1137/s0040585x97t991684
E. A. Feinberg, A. N. Shiryaev
{"title":"On Forward and Backward Kolmogorov Equations for Pure Jump Markov Processes and Their Generalizations","authors":"E. A. Feinberg, A. N. Shiryaev","doi":"10.1137/s0040585x97t991684","DOIUrl":"https://doi.org/10.1137/s0040585x97t991684","url":null,"abstract":"Theory of Probability &amp;Its Applications, Volume 68, Issue 4, Page 643-656, February 2024. <br/> In the present paper, we first give a survey of the forward and backward Kolmogorov equations for pure jump Markov processes with finite and countable state spaces, and then describe relevant results for the case of Markov processes with values in standard Borel spaces based on results of W. Feller and the authors of the present paper.","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139770961","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}
引用次数: 0
Weakly Supercritical Branching Process in a Random Environment Dying at a Distant Moment 随机环境中的弱超临界分支过程在遥远时刻消亡
IF 0.6 4区 数学
Theory of Probability and its Applications Pub Date : 2024-02-07 DOI: 10.1137/s0040585x97t991611
V. I. Afanasyev
{"title":"Weakly Supercritical Branching Process in a Random Environment Dying at a Distant Moment","authors":"V. I. Afanasyev","doi":"10.1137/s0040585x97t991611","DOIUrl":"https://doi.org/10.1137/s0040585x97t991611","url":null,"abstract":"Theory of Probability &amp;Its Applications, Volume 68, Issue 4, Page 537-558, February 2024. <br/> A functional limit theorem is proved for a weakly supercritical branching process in a random environment under the condition that the process becomes extinct after time $nto infty $.","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139769299","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}
引用次数: 0
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