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Uniform Cramer moderate deviations and Berry-Esseen bounds for a supercritical branching process in a random environment

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Frontiers of Mathematics in China 2020年第5期15卷 891-914页

作者： xiequan fan Haijuan HU Quansheng LIU Center for Applied Mathematics Tianjin UniversityTianjin 300072China School of Mathematics and Statistics Northeastern University at QinhuangdaoQinhuangdao 066004China Universite de Bretagne-Sud LMBAUMR CNRS 6205Campus de Tohannic56017 VannesFrance School of Statistics and Mathematics Zhongnan University of Economics and LawWuhan 430073China

Let{Zn,n≥0}be a supercritical branching process in an independent and identically distributed random *** prove Cramer moderate deviations and Berry-Esseen bounds for log(Zn+n0/Zn0)uniformly in n0∈N,which extend the corresponding results by ***,***,and ***[Stochastic ***.,2017,127:1255-1281]established for n0=*** extension is interesting in theory,and is motivated by applications.A new method is developed for the proofs;some conditions of Grama et *** relaxed in our present *** example of application is given in constructing confidence intervals to estimate the criticality parameter in terms of log(Zn+n0/Zn0)and n.

关键词： Branching processes random environment Cramer moderatedeviations Berry-Esseen bounds

Normalized and self-normalized Cramér-type moderate deviations for the Euler-Maruyama scheme for the SDE

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Science China Mathematics 2024年第8期67卷 1865-1880页

作者： xiequan fan Haijuan Hu Lihu Xu Center for Applied Mathematics Tianjin UniversityTianjin 300072China School of Mathematics and Statistics Northeastern University at QinhuangdaoQinhuangdao 066004China Department of Mathematics Faculty of Science and TechnologyUniversity of MacaoMacaoChina

In this paper,we establish normalized and self-normalized Cramér-type moderate deviations for the Euler-Maruyama scheme for *** to our results,Berry-Esseen's bounds and moderate deviation principles are also *** norm... 详细信息

关键词： Euler-Maruyama scheme Cramer-type moderate deviations self-normalized sequences Berry-Esseen’s bounds

Berry-Esseen Bounds for Self-Normalized Martingales

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Communications in Mathematics and Statistics 2018年第1期6卷 13-27页

作者： xiequan fan Qi-Man Shao Center for Applied Mathematics Tianjin UniversityTianjin 300072China Department of Statistics Chinese University of Hong KongShatinNTHong Kong

A Berry–Esseen bound is obtained for self-normalized martingales under the assumption of finite *** bound coincides with the classical Berry–*** of the *** to Student’s statistic and autoregressive process are also... 详细信息

关键词： Self-normalized process Berry-Esseen bounds Martingales Student’s statistic Autoregressive process

Sharp large deviation results for sums of independent random variables

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Science China Mathematics 2015年第9期58卷 1939-1958页

作者： fan xiequan GRAMA Ion LIU QuanSheng Regularity Team Institut National de Recherche en Informatique et en Automatique Laboratoire de Mathmatiques Appliques aux Systèmes Ecole Centrale Paris-Grande Voie des Vignes Laboratoire de Mathmatiques de Bretagne Atlantique UMR 6205 University Bretagne-Sud School of Mathematics and Computing Science Changsha University of Science and Technology

We show sharp bounds for probabilities of large deviations for sums of independent random variables satisfying Bernstein's condition. One such bound is very close to the tail of the standard Gaussian law in certain case; other bounds improve the inequalities of Bennett and Hoeffding by adding missing factors in the spirit of Talagrand(1995). We also complete Talagrand's inequality by giving a lower bound of the same form, leading to an equality. As a consequence, we obtain large deviation expansions similar to those of Cram′er(1938),Bahadur-Rao(1960) and Sakhanenko(1991). We also show that our bound can be used to improve a recent inequality of Pinelis(2014).

关键词： Bernstein’s inequality sharp large deviations Cramér large deviations expansion of BahadurRao sums of independent random variabl

Wasserstein-1 Distance and Nonuniform Berry-Esseen Bound for a Supercritical Branching Process in a Random Environment

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Journal of Mathematical Research with Applications 2023年第6期43卷 737-753页

作者： Hao WU xiequan fan Zhiqiang GAO Yinna YE Center for Applied Mathematics Tianjin University School of Mathematics and Statistics Northeastern University at Qinhuangdao Laboratory of Mathematics and Complex Systems School of Mathematical SciencesBeijing Normal University Department of Applied Mathematics School of Mathematics and PhysicsXi'an Jiaotong-Liverpool University

Let(Zn)n≥0be a supercritical branching process in an independent and identically distributed random environment. We establish an optimal convergence rate in the Wasserstein-1 distance for the process(Zn)n≥0, which completes a result of Grama et al. [Stochastic ***., 2017, 127(4): 1255–1281]. Moreover, an exponential nonuniform Berry-Esseen bound is also given. At last, some applications of the main results to the confidence interval estimation for the criticality parameter and the population size Znare discussed.

关键词： Branching processes Random environment Wasserstein-1 distance Nonuniform Berry-Esseen bounds

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随机环境下两个上临界分支过程的参数比较

数学物理学报（A辑） 2023年第5期43卷 1440-1470页

作者：范协铨胡海娟吴浩叶印娜东北大学秦皇岛分校数学与统计学院河北秦皇岛066003 天津大学应用数学中心天津300072 西交利物浦大学数学物理学院江苏苏州215123

设(Z_(1,n))_(n≥0)和(Z_(2,n))_(n≥0)是两个在独立同分布随机环境下的上临界分支过程,并且其关键参数分别为μ1和μ2.容易知道,在适当条件下,1/nlnZ_(1,n)和1/mlnZ_(2,m)分别依概率收敛到μ1和μ2.该文旨在讨论两个上临界分支过程的... 详细信息

设(Z_(1,n))_(n≥0)和(Z_(2,n))_(n≥0)是两个在独立同分布随机环境下的上临界分支过程,并且其关键参数分别为μ1和μ2.容易知道,在适当条件下,1/nlnZ_(1,n)和1/mlnZ_(2,m)分别依概率收敛到μ1和μ2.该文旨在讨论两个上临界分支过程的关键参数之差μ1−μ2的估计问题,它可以被看作是一类双样本U统计量问题.我们得到了1/nlnZ_(1,n−1/m)lnZ_(2,m)的中心极限定理,非一致性Berry-Esseen估计和Cramér型中偏差.最后,作为应用部分,指出了以上的结果可用于关键参数置信区间的构造.

关键词：分支过程随机环境 Berry-Esseen 估计 Cramér 型中偏差

Soluble epoxide hydrolase:a next-generation drug target for Alzheimer's disease and related dementias

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Neural Regeneration Research 2025年第9期20卷 2585-2586页

作者： Andrew Gregory Chengyun Tang fan fan Department of Physiology Medical College of GeorgiaAugusta UniversityAugustaGAUSA

Alzheimer's disease(AD)and Alzheimer's diseaserelated dementias(ADRD)represent a significant public health challenge,with projections indicating a substantial increase in affected individuals due to the aging global *** the World Health Organization,AD/ADRD has affected more than 55 million individuals worldwide,with an additional 10 million cases diagnosed each year.

关键词： Alzheimer population drug

Tackling the microlensing wave effects of strong lensing gravitational waves with TAAH

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Science China(Physics,Mechanics & Astronomy) 2025年第1期Mechanics & Astronomy) .卷 257-258页

作者： Zuhui fan South-Western Institute for Astronomy Research Yunnan University

The rapid development of gravitational wave（GW） observations since their first detection in 2015 [1] has opened a completely new window for exploring the Universe. Consequently, astronomical research has entered the multimessenger era, allowing us to use different tracers to view the cosmos from various perspectives. Among others, the appealing application of gravitational wave events from compact binary mergers is that they can act as standard sirens to determine absolute cosmic distances entirely independent of standard candles. This approach is one of the most promising means to solve the current H0tension problem.

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Bandgap characteristics analysis and graded design of a novel metamaterial for flexural wave suppression

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Applied Mathematics and Mechanics(English Edition) 2025年第1期46卷 1-24页

作者： fan YANG Zhaoyang MA Xingming GUO Shanghai Key Laboratory of Mechanics in Energy Engineering Shanghai Institute of Applied Mathematics and Mechanics School of Mechanics and Engineering ScienceShanghai University Shanghai Institute of Aircraft Mechanics and Control

A novel elastic metamaterial is proposed with the aim of achieving lowfrequency broad bandgaps and bandgap regulation. The band structure of the proposed metamaterial is calculated based on the Floquet-Bloch theorem, and the boundary modes of each bandgap are analyzed to understand the effects of each component of the unit cell on the bandgap formation. It is found that the metamaterials with a low elastic modulus of ligaments can generate flexural wave bandgaps below 300 Hz. Multi-frequency vibrations can be suppressed through the selective manipulation of bandgaps. The dual-graded design of metamaterials that can significantly improve the bandgap width is proposed based on parametric studies. A new way that can regulate the bandgap is revealed by studying the graded elastic modulus in the substrate. The results demonstrate that the nonlinear gradient of the elastic modulus in the substrate offers better bandgap performance. Based on these analyses, the proposed elastic metamaterials can pave the way for multi-frequency vibration control, low-frequency bandgap broadening, and bandgap tuning.

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