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Theory of Probability and its Applications最新文献

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Universal Nonparametric Kernel-Type Estimators for the Mean and Covariance Functions of a Stochastic Process 随机过程均值和协方差函数的通用非参数核型估计器
IF 0.6 4区 数学
Theory of Probability and its Applications Pub Date : 2024-05-02 DOI: 10.1137/s0040585x97t991738
Yu. Yu. Linke, I. S. Borisov
{"title":"Universal Nonparametric Kernel-Type Estimators for the Mean and Covariance Functions of a Stochastic Process","authors":"Yu. Yu. Linke, I. S. Borisov","doi":"10.1137/s0040585x97t991738","DOIUrl":"https://doi.org/10.1137/s0040585x97t991738","url":null,"abstract":"Theory of Probability &amp;Its Applications, Volume 69, Issue 1, Page 35-58, May 2024. <br/> Let $f_1(t), dots, f_n(t)$ be independent copies of some a.s. continuous stochastic process $f(t)$, $tin[0,1]$, which are observed with noise. We consider the problem of nonparametric estimation of the mean function $mu(t) = mathbf{E}f(t)$ and of the covariance function $psi(t,s)=operatorname{Cov}{f(t),f(s)}$ if the noise values of each of the copies $f_i(t)$, $i=1,dots,n$, are observed in some collection of generally random (in general) time points (regressors). Under wide assumptions on the time points, we construct uniformly consistent kernel estimators for the mean and covariance functions both in the case of sparse data (where the number of observations for each copy of the stochastic process is uniformly bounded) and in the case of dense data (where the number of observations at each of $n$ series is increasing as $ntoinfty$). In contrast to the previous studies, our kernel estimators are universal with respect to the structure of time points, which can be either fixed rather than necessarily regular, or random rather than necessarily formed of independent or weakly dependent random variables.","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":"9 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140839317","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
Limit Behavior of Order Statistics on Cycle Lengths of Random $A$-Permutations 随机 $A$-Permutations 循环长度的阶次统计极限行为
IF 0.6 4区 数学
Theory of Probability and its Applications Pub Date : 2024-05-02 DOI: 10.1137/s0040585x97t991787
A. L. Yakymiv
{"title":"Limit Behavior of Order Statistics on Cycle Lengths of Random $A$-Permutations","authors":"A. L. Yakymiv","doi":"10.1137/s0040585x97t991787","DOIUrl":"https://doi.org/10.1137/s0040585x97t991787","url":null,"abstract":"Theory of Probability &amp;Its Applications, Volume 69, Issue 1, Page 117-126, May 2024. <br/> We consider a random permutation $tau_n$ uniformly distributed on the set of all permutations of degree $n$ whose cycle lengths lie in a fixed set $A$ (the so-called $A$-permutations). Let $zeta_n$ be the total number of cycles, and let $eta_n(1)leqeta_n(2)leqdotsleqeta_n(zeta_n)$ be the ordered sample of cycle lengths of the permutation $tau_n$. We consider a class of sets $A$ with positive density in the set of natural numbers. We study the asymptotic behavior of $eta_n(m)$ with numbers $m$ in the left-hand and middle parts of this series for a class of sets of positive asymptotic density. A limit theorem for the rightmost terms of this series was proved by the author of this note earlier. The study of limit properties of the sequence $eta_n(m)$ dates back to the paper by Shepp and Lloyd [Trans. Amer. Math. Soc., 121 (1966), pp. 340--357] who considered the case $A=mathbf N$.","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":"64 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140839363","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 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":"67 1","pages":""},"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":"1 1","pages":""},"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
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":"51 1","pages":""},"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":"96 1","pages":""},"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":"7 1","pages":""},"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":"21 1","pages":""},"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":"20 1","pages":""},"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":"17 1","pages":""},"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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