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Uniqueness of the Inverse First-Passage Time Problem and the Shape of the Shiryaev Boundary 逆首次通过时间问题的唯一性和Shiryaev边界的形状
4区 数学
Theory of Probability and its Applications Pub Date : 2023-02-01 DOI: 10.1137/s0040585x97t991155
A. Klump, M. Kolb
{"title":"Uniqueness of the Inverse First-Passage Time Problem and the Shape of the Shiryaev Boundary","authors":"A. Klump, M. Kolb","doi":"10.1137/s0040585x97t991155","DOIUrl":"https://doi.org/10.1137/s0040585x97t991155","url":null,"abstract":"Given a distribution on the positive extended real line, the two-sided inverse first-passage time problem for Brownian motion asks for a function such that the first passage time of this function by a reflected Brownian motion has the given distribution. We combine the ideas of Ekström and Janson, which were developed within the scope of the one-sided inverse first-passage time problem, with the methods of De Masi et al., which were used in the context of free boundary problems, in order to give a different proof for the uniqueness for the two-sided inverse first-passage time problem by using a stochastic order relation. We provide criteria for qualitative properties of solutions of the inverse first-passage problem, which apply to the boundary corresponding to the exponential distribution.","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135962649","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: 1
Abstracts of Talks Given at the 7th International Conference on Stochastic Methods, I 在第七届国际随机方法会议上的报告摘要
4区 数学
Theory of Probability and its Applications Pub Date : 2023-02-01 DOI: 10.1137/s0040585x97t991210
A. N. Shiryaev, I. V. Pavlov
{"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":"59 1","pages":"0"},"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}
引用次数: 1
Partial Linear Eigenvalue Statistics for Non-Hermitian Random Matrices 非厄米随机矩阵的部分线性特征值统计
4区 数学
Theory of Probability and its Applications Pub Date : 2023-02-01 DOI: 10.1137/s0040585x97t991179
S. O'Rourke, N. Williams
{"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":"11 1","pages":"0"},"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}
引用次数: 0
Normal Limit Law for Protected Node Profile of Random Recursive Trees 随机递归树保护节点轮廓的正规极限律
IF 0.6 4区 数学
Theory of Probability and its Applications Pub Date : 2022-11-07 DOI: 10.1137/s0040585x97t991040
J. Toofanpour, M. Javanian, R. Imany-Nabiyyi
{"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 &amp;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":"13 1","pages":""},"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}
引用次数: 0
Mallows Distance Convergence for Extremes: Regeneration Approach 极值的Mallows距离收敛:再生方法
IF 0.6 4区 数学
Theory of Probability and its Applications Pub Date : 2022-11-07 DOI: 10.1137/s0040585x97t991076
S. Mousavinasr, C. R. Gonçalves, C. C. Y. Dorea
{"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 &amp;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":"45 1","pages":""},"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}
引用次数: 0
Generalized Marcinkiewicz Laws for Weighted Dependent Random Vectors in Hilbert Spaces Hilbert空间中加权相关随机向量的广义Marcinkiewicz定律
IF 0.6 4区 数学
Theory of Probability and its Applications Pub Date : 2022-11-07 DOI: 10.1137/s0040585x97t991039
T. C. Son, L. V. Dung, D. T. Dat, T. T. Trang
{"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 &amp;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":"24 1","pages":""},"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}
引用次数: 0
A Note on the Berry--Esseen Bounds for $rho$-Mixing Random Variables and Their Applications $rho$-混合随机变量的Berry- Esseen界及其应用
IF 0.6 4区 数学
Theory of Probability and its Applications Pub Date : 2022-11-07 DOI: 10.1137/s0040585x97t991027
C. Lu, W. Yu, R. L. Ji, H. L. Zhou, X. J. Wang
{"title":"A Note on the Berry--Esseen Bounds for $rho$-Mixing Random Variables and Their Applications","authors":"C. Lu, W. Yu, R. L. Ji, H. L. Zhou, X. J. Wang","doi":"10.1137/s0040585x97t991027","DOIUrl":"https://doi.org/10.1137/s0040585x97t991027","url":null,"abstract":"Theory of Probability &amp;Its Applications, Volume 67, Issue 3, Page 415-433, November 2022. <br/> 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.","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":"59 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138539723","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
Mallows Distance Convergence for Extremes: Regeneration Approach 极值的Mallows距离收敛:再生方法
IF 0.6 4区 数学
Theory of Probability and its Applications Pub Date : 2022-11-07 DOI: 10.1137/s0040585x97t991076
S. Mousavinasr, C. R. Gonçalves, C. C. Y. Dorea
{"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 &amp;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":"45 1","pages":""},"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}
引用次数: 0
A Gibbs Conditional Theorem under Extreme Deviation 极值偏差下的吉布斯条件定理
IF 0.6 4区 数学
Theory of Probability and its Applications Pub Date : 2022-11-07 DOI: 10.1137/s0040585x97t991015
M. Biret, M. Broniatowski, Z. Cao
{"title":"A Gibbs Conditional Theorem under Extreme Deviation","authors":"M. Biret, M. Broniatowski, Z. Cao","doi":"10.1137/s0040585x97t991015","DOIUrl":"https://doi.org/10.1137/s0040585x97t991015","url":null,"abstract":"Theory of Probability &amp;Its Applications, Volume 67, Issue 3, Page 389-414, November 2022. <br/> 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.","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":"13 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138539666","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
Normal Limit Law for Protected Node Profile of Random Recursive Trees 随机递归树保护节点轮廓的正规极限律
IF 0.6 4区 数学
Theory of Probability and its Applications Pub Date : 2022-11-07 DOI: 10.1137/s0040585x97t991040
J. Toofanpour, M. Javanian, R. Imany-Nabiyyi
{"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 &amp;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":"13 1","pages":""},"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}
引用次数: 0
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