Pub Date : 2023-02-01DOI: 10.1137/s0040585x97t991210
A. N. Shiryaev, I. V. Pavlov
This paper presents abstracts of talks given at the 7th International Conference on Stochastic Methods (ICSM-7), held June 2--9, 2022 at Divnomorskoe (near the town of Gelendzhik) at the Raduga sports and fitness center of the Don State Technical University. The conference was chaired by A. N. Shiryaev. Participants included leading scientists from Russia, France, Portugal, and Tadjikistan.
本文介绍了2022年6月2日至9日在顿河国立技术大学Raduga体育健身中心的Divnomorskoe (Gelendzhik镇附近)举行的第七届国际随机方法会议(ICSM-7)上的演讲摘要。会议由A. N. Shiryaev主持。与会者包括来自俄罗斯、法国、葡萄牙和塔吉克斯坦的顶尖科学家。
{"title":"Abstracts of Talks Given at the 7th International Conference on Stochastic Methods, I","authors":"A. N. Shiryaev, I. V. Pavlov","doi":"10.1137/s0040585x97t991210","DOIUrl":"https://doi.org/10.1137/s0040585x97t991210","url":null,"abstract":"This paper presents abstracts of talks given at the 7th International Conference on Stochastic Methods (ICSM-7), held June 2--9, 2022 at Divnomorskoe (near the town of Gelendzhik) at the Raduga sports and fitness center of the Don State Technical University. The conference was chaired by A. N. Shiryaev. Participants included leading scientists from Russia, France, Portugal, and Tadjikistan.","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135962650","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 : 2023-02-01DOI: 10.1137/s0040585x97t991179
S. O'Rourke, N. Williams
For an $n times n$ independent-entry random matrix $X_n$ with eigenvalues $lambda_1, dots, lambda_n$, the seminal work of Rider and Silverstein [Ann. Probab., 34 (2006), pp. 2118--2143] asserts that the fluctuations of the linear eigenvalue statistics $sum_{i=1}^n f(lambda_i)$ converge to a Gaussian distribution for sufficiently nice test functions $f$. We study the fluctuations of $sum_{i=1}^{n-K} f(lambda_i)$, where $K$ randomly chosen eigenvalues have been removed from the sum. In this case, we identify the limiting distribution and show that it need not be Gaussian. Our results hold for the case when $K$ is fixed as well as for the case when $K$ tends to infinity with $n$. The proof utilizes the predicted locations of the eigenvalues introduced by E. Meckes and M. Meckes, [Ann. Fac. Sci. Toulouse Math. (6), 24 (2015), pp. 93--117]. As a consequence of our methods, we obtain a rate of convergence for the empirical spectral distribution of $X_n$ to the circular law in Wasserstein distance, which may be of independent interest.
对于具有特征值的$n times n$独立入口随机矩阵$X_n$$lambda_1, dots, lambda_n$, Rider和Silverstein的开创性工作[Ann。可能吧。[j]， 34 (2006)， pp. 2118—2143]断言，对于足够好的测试函数$f$，线性特征值统计量的波动收敛于高斯分布$sum_{i=1}^n f(lambda_i)$。我们研究了$sum_{i=1}^{n-K} f(lambda_i)$的波动，其中$K$随机选择的特征值已经从和中去除。在这种情况下，我们确定了极限分布，并证明它不一定是高斯分布。我们的结果既适用于$K$固定的情况，也适用于$K$随$n$趋于无穷大的情况。该证明利用了E. Meckes和M. Meckes， [Ann。]脸。科学。图卢兹数学。(6)， 24 (2015)， pp. 93—117]。由于我们的方法，我们得到了在Wasserstein距离上循环定律的经验谱分布$X_n$的收敛速率，这可能是独立的兴趣。
{"title":"Partial Linear Eigenvalue Statistics for Non-Hermitian Random Matrices","authors":"S. O'Rourke, N. Williams","doi":"10.1137/s0040585x97t991179","DOIUrl":"https://doi.org/10.1137/s0040585x97t991179","url":null,"abstract":"For an $n times n$ independent-entry random matrix $X_n$ with eigenvalues $lambda_1, dots, lambda_n$, the seminal work of Rider and Silverstein [Ann. Probab., 34 (2006), pp. 2118--2143] asserts that the fluctuations of the linear eigenvalue statistics $sum_{i=1}^n f(lambda_i)$ converge to a Gaussian distribution for sufficiently nice test functions $f$. We study the fluctuations of $sum_{i=1}^{n-K} f(lambda_i)$, where $K$ randomly chosen eigenvalues have been removed from the sum. In this case, we identify the limiting distribution and show that it need not be Gaussian. Our results hold for the case when $K$ is fixed as well as for the case when $K$ tends to infinity with $n$. The proof utilizes the predicted locations of the eigenvalues introduced by E. Meckes and M. Meckes, [Ann. Fac. Sci. Toulouse Math. (6), 24 (2015), pp. 93--117]. As a consequence of our methods, we obtain a rate of convergence for the empirical spectral distribution of $X_n$ to the circular law in Wasserstein distance, which may be of independent interest.","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136178389","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 : 2022-11-07DOI: 10.1137/s0040585x97t991040
J. Toofanpour, M. Javanian, R. Imany-Nabiyyi
Theory of Probability &Its Applications, Volume 67, Issue 3, Page 452-464, November 2022. Protected nodes, i.e., nodes with distance at least 2 to each leaf, have been studied in various classes of random rooted trees. In this short note, we investigate the protected node profile, i.e., the number of protected nodes with the same distance from the root in random recursive trees. Here, when the limit ratio of the level and logarithm of tree size is zero, we present the asymptotic expectations, variances, and covariance of the protected node profile and the nonprotected node profile in random recursive trees. We also show that protected node and nonprotected node profiles have a bivariate normal limiting distribution via the joint characteristic function and singularity analysis.
{"title":"Normal Limit Law for Protected Node Profile of Random Recursive Trees","authors":"J. Toofanpour, M. Javanian, R. Imany-Nabiyyi","doi":"10.1137/s0040585x97t991040","DOIUrl":"https://doi.org/10.1137/s0040585x97t991040","url":null,"abstract":"Theory of Probability &Its Applications, Volume 67, Issue 3, Page 452-464, November 2022. <br/> Protected nodes, i.e., nodes with distance at least 2 to each leaf, have been studied in various classes of random rooted trees. In this short note, we investigate the protected node profile, i.e., the number of protected nodes with the same distance from the root in random recursive trees. Here, when the limit ratio of the level and logarithm of tree size is zero, we present the asymptotic expectations, variances, and covariance of the protected node profile and the nonprotected node profile in random recursive trees. We also show that protected node and nonprotected node profiles have a bivariate normal limiting distribution via the joint characteristic function and singularity analysis.","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138539717","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 : 2022-11-07DOI: 10.1137/s0040585x97t991076
S. Mousavinasr, C. R. Gonçalves, C. C. Y. Dorea
Theory of Probability &Its Applications, Volume 67, Issue 3, Page 478-484, November 2022. We explore the Mallows distance convergence to characterize the domain of attraction for extreme value distributions. Under mild assumptions we derive the necessary and sufficient conditions. In addition to the i.i.d. case, our results apply to regenerative processes.
{"title":"Mallows Distance Convergence for Extremes: Regeneration Approach","authors":"S. Mousavinasr, C. R. Gonçalves, C. C. Y. Dorea","doi":"10.1137/s0040585x97t991076","DOIUrl":"https://doi.org/10.1137/s0040585x97t991076","url":null,"abstract":"Theory of Probability &Its Applications, Volume 67, Issue 3, Page 478-484, November 2022. <br/> We explore the Mallows distance convergence to characterize the domain of attraction for extreme value distributions. Under mild assumptions we derive the necessary and sufficient conditions. In addition to the i.i.d. case, our results apply to regenerative processes.","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138539758","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 : 2022-11-07DOI: 10.1137/s0040585x97t991039
T. C. Son, L. V. Dung, D. T. Dat, T. T. Trang
Theory of Probability &Its Applications, Volume 67, Issue 3, Page 434-451, November 2022. The aim of this paper is to apply the theory of regularly varying functions for studying Marcinkiewicz weak and strong laws of large numbers for the weighted sum $S_n=sum_{j=1}^{m_n}c_{nj}X_j$, where $(X_n;, ngeq 1)$ is a sequence of dependent random vectors in Hilbert spaces, and $(c_{nj})$ is an array of real numbers. Moreover, these results are applied to obtain some results on the convergence of multivariate Pareto--Zipf distributions and multivariate log-gamma distributions.
{"title":"Generalized Marcinkiewicz Laws for Weighted Dependent Random Vectors in Hilbert Spaces","authors":"T. C. Son, L. V. Dung, D. T. Dat, T. T. Trang","doi":"10.1137/s0040585x97t991039","DOIUrl":"https://doi.org/10.1137/s0040585x97t991039","url":null,"abstract":"Theory of Probability &Its Applications, Volume 67, Issue 3, Page 434-451, November 2022. <br/> The aim of this paper is to apply the theory of regularly varying functions for studying Marcinkiewicz weak and strong laws of large numbers for the weighted sum $S_n=sum_{j=1}^{m_n}c_{nj}X_j$, where $(X_n;, ngeq 1)$ is a sequence of dependent random vectors in Hilbert spaces, and $(c_{nj})$ is an array of real numbers. Moreover, these results are applied to obtain some results on the convergence of multivariate Pareto--Zipf distributions and multivariate log-gamma distributions.","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138539681","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 : 2022-11-07DOI: 10.1137/s0040585x97t991027
C. Lu, W. Yu, R. L. Ji, H. L. Zhou, X. J. Wang
Theory of Probability &Its Applications, Volume 67, Issue 3, Page 415-433, November 2022. Recently, Wang and Hu [Theory Probab. Appl., 63 (2019), pp. 479--499] established the Berry--Esseen bounds for $rho$-mixing random variables (r.v.'s) with the rate of normal approximation $O(n^{-1/6}log n)$ by using the martingale method. In this paper, we establish some general results on the rates of normal approximation, which include the corresponding ones of Wang and Hu. The rate can be as high as $O(n^{-1/5})$ or $O(n^{-1/4}log^{1/2} n)$ under some suitable conditions. As applications, we obtain the Berry--Esseen bounds of sample quantiles based on $rho$-mixing random samples. Finally, we also present some numerical simulations to demonstrate finite sample performances of the theoretical result.
概率论及其应用，第67卷，第3期，第415-433页，2022年11月。最近，王和胡[理论概率。苹果。[j]， 63 (2019)， pp. 479—499]通过使用鞅方法建立了$rho$ -混合随机变量(r.v.s)的Berry—Esseen界，其正态逼近率为$O(n^{-1/6}log n)$。本文建立了一些关于正态逼近速率的一般结果，其中包括Wang和Hu的相应结果。在适当的条件下，速率可高达$O(n^{-1/5})$或$O(n^{-1/4}log^{1/2} n)$。作为应用，我们得到了基于$rho$混合随机样本的样本分位数的Berry—Esseen界。最后，通过数值模拟验证了理论结果的有限样本性能。
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Pub Date : 2022-11-07DOI: 10.1137/s0040585x97t991076
S. Mousavinasr, C. R. Gonçalves, C. C. Y. Dorea
Theory of Probability &Its Applications, Volume 67, Issue 3, Page 478-484, November 2022. We explore the Mallows distance convergence to characterize the domain of attraction for extreme value distributions. Under mild assumptions we derive the necessary and sufficient conditions. In addition to the i.i.d. case, our results apply to regenerative processes.
{"title":"Mallows Distance Convergence for Extremes: Regeneration Approach","authors":"S. Mousavinasr, C. R. Gonçalves, C. C. Y. Dorea","doi":"10.1137/s0040585x97t991076","DOIUrl":"https://doi.org/10.1137/s0040585x97t991076","url":null,"abstract":"Theory of Probability &Its Applications, Volume 67, Issue 3, Page 478-484, November 2022. <br/> We explore the Mallows distance convergence to characterize the domain of attraction for extreme value distributions. Under mild assumptions we derive the necessary and sufficient conditions. In addition to the i.i.d. case, our results apply to regenerative processes.","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138539745","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 : 2022-11-07DOI: 10.1137/s0040585x97t991015
M. Biret, M. Broniatowski, Z. Cao
Theory of Probability &Its Applications, Volume 67, Issue 3, Page 389-414, November 2022. We explore some properties of the conditional distribution of an independently and identically distributed (i.i.d.) sample under large exceedances of its sum. Thresholds for the asymptotic independence of the summands are observed, in contrast with the classical case when the conditioning event is in the range of a large deviation. This paper is an extension of Broniatowski and Cao [Extremes, 17 (2014), pp. 305--336]. Tools include a new Edgeworth expansion adapted to specific triangular arrays, where the rows are generated by tilted distribution with diverging parameters, and some Abelian type results.
概率论及其应用，67卷，第3期，389-414页，2022年11月。研究了独立同分布(i.i.d)样本在其和的大超出下的条件分布的一些性质。与经典情况相比，当条件作用事件在较大偏差范围内时，观察到求和的渐近独立性的阈值。本文是Broniatowski和Cao [Extremes, 17 (2014)， pp. 305—336]的延伸。工具包括一个新的Edgeworth扩展，适用于特定的三角形数组，其中行是由具有发散参数的倾斜分布产生的，以及一些阿贝尔类型的结果。
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Pub Date : 2022-11-07DOI: 10.1137/s0040585x97t991040
J. Toofanpour, M. Javanian, R. Imany-Nabiyyi
Theory of Probability &Its Applications, Volume 67, Issue 3, Page 452-464, November 2022. Protected nodes, i.e., nodes with distance at least 2 to each leaf, have been studied in various classes of random rooted trees. In this short note, we investigate the protected node profile, i.e., the number of protected nodes with the same distance from the root in random recursive trees. Here, when the limit ratio of the level and logarithm of tree size is zero, we present the asymptotic expectations, variances, and covariance of the protected node profile and the nonprotected node profile in random recursive trees. We also show that protected node and nonprotected node profiles have a bivariate normal limiting distribution via the joint characteristic function and singularity analysis.
{"title":"Normal Limit Law for Protected Node Profile of Random Recursive Trees","authors":"J. Toofanpour, M. Javanian, R. Imany-Nabiyyi","doi":"10.1137/s0040585x97t991040","DOIUrl":"https://doi.org/10.1137/s0040585x97t991040","url":null,"abstract":"Theory of Probability &Its Applications, Volume 67, Issue 3, Page 452-464, November 2022. <br/> Protected nodes, i.e., nodes with distance at least 2 to each leaf, have been studied in various classes of random rooted trees. In this short note, we investigate the protected node profile, i.e., the number of protected nodes with the same distance from the root in random recursive trees. Here, when the limit ratio of the level and logarithm of tree size is zero, we present the asymptotic expectations, variances, and covariance of the protected node profile and the nonprotected node profile in random recursive trees. We also show that protected node and nonprotected node profiles have a bivariate normal limiting distribution via the joint characteristic function and singularity analysis.","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138539672","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 : 2022-11-07DOI: 10.1137/s0040585x97t991027
C. Lu, W. Yu, R. L. Ji, H. L. Zhou, X. J. Wang
Theory of Probability &Its Applications, Volume 67, Issue 3, Page 415-433, November 2022. Recently, Wang and Hu [Theory Probab. Appl., 63 (2019), pp. 479--499] established the Berry--Esseen bounds for $rho$-mixing random variables (r.v.'s) with the rate of normal approximation $O(n^{-1/6}log n)$ by using the martingale method. In this paper, we establish some general results on the rates of normal approximation, which include the corresponding ones of Wang and Hu. The rate can be as high as $O(n^{-1/5})$ or $O(n^{-1/4}log^{1/2} n)$ under some suitable conditions. As applications, we obtain the Berry--Esseen bounds of sample quantiles based on $rho$-mixing random samples. Finally, we also present some numerical simulations to demonstrate finite sample performances of the theoretical result.
概率论及其应用，第67卷，第3期，第415-433页，2022年11月。最近，王和胡[理论概率。苹果。[j]， 63 (2019)， pp. 479—499]通过使用鞅方法建立了$rho$ -混合随机变量(r.v.s)的Berry—Esseen界，其正态逼近率为$O(n^{-1/6}log n)$。本文建立了一些关于正态逼近速率的一般结果，其中包括Wang和Hu的相应结果。在适当的条件下，速率可高达$O(n^{-1/5})$或$O(n^{-1/4}log^{1/2} n)$。作为应用，我们得到了基于$rho$混合随机样本的样本分位数的Berry—Esseen界。最后，通过数值模拟验证了理论结果的有限样本性能。
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