Elementary renewal theorems for widely dependent random variables with applications to precise large deviations

Abstract

On the basis of Wang and Cheng (J. Math. Anal. Appl. 384 (2011) 597–606), this paper further investigates elementary renewal theorems for counting processes generated by random walks with widely orthant dependent increments. The obtained results improve the corresponding ones of the above-mentioned paper mainly in the sense of weakening the moment conditions on the positive parts of the increments. Meanwhile, a revised version of strong law of large numbers for random walks with widely orthant dependent increments is established, which improves Theorem 1.4 of Wang and Cheng (2011 Wang, Y., and D. Cheng. 2011. Basic renewal theorems for a random walk with widely dependent increments and their applications. Journal of Mathematical Analysis and Applications 384 (2):597–606. doi:10.1016/j.jmaa.2011.06.010.[Crossref], [Web of Science ®] , [Google Scholar]) by enlarging the regions of dominating coefficients. Finally, by using the above results, some precise large deviation results for a nonstandard renewal risk model are established, in which the innovations are widely orthant dependent random variables with common heavy tails, and the inter-arrival times are also widely orthant dependent.     

《孟子》释读辨误(四则)

传统经典须细读，在细读的基础上领会真义。历代注家对《孟子》的注疏多有误读之处，如"攘"，本义为"取自来之物"，经"多少同盗"，演变为"攘"即"盗"；"巨室"初谓国君住的大房子，这里当喻指国君，但注家多强解为指大臣；舜在"完廪""浚井"的过程中是如何脱难的，本文没有说，注家依据其他材料做了合理化解读，未必符合本义。"坏宫室以为汙池"，如从人类社会发展史的角度来释读，实际上是要维持以渔猎为生的生存方式。致误的根源有"非黑即白"的思维方式、前后矛盾、对古代"不雅驯"的文字进行改造等。     

Information in Tender Offers With a Large Shareholder

We study takeovers of firms whose ownership structure is a mixture of minority block‐holders and small shareholders. We show that the combination of dispersed private information on the side of small shareholders and the presence of a large shareholder can facilitate profitable takeovers. Furthermore, our analysis implies that even if some model of takeovers predicts a profit for the raider, for example, due to private benefits, the profit will be underestimated unless the large shareholder and the dispersion of information among the small shareholders are modeled.     

A strong law of large numbers for independent random variables under non-additive probabilities

Abstract

Under non‐additive probabilities, cluster points of the empirical average have been proved to quasi-surely fall into the interval constructed by either the lower and upper expectations or the lower and upper Choquet expectations. In this paper, based on the initiated notion of independence, we obtain a different Marcinkiewicz-Zygmund type strong law of large numbers. Then the Kolmogorov type strong law of large numbers can be derived from it directly, stating that the closed interval between the lower and upper expectations is the smallest one that covers cluster points of the empirical average quasi-surely.     

一类含有随机参数的混沌系统的Hopf分岔研究

文章选取随机变量为系统的随机变量研究含有随机参数混沌系统的Hopf分岔,利用Chebyshev正交多项式逼近理论将含有随机变量的系统转化为等价的确定性系统,通过Hopf分岔定理和Lyapunov系数讨论了随机参数系统的Hopf分岔及稳定性,发现随机系统的渐进稳定性参数区间大小不仅和确定性参数有关,还与随机参数有非常密切的关系.     

浅埋大跨黄土隧道下穿公路方案比选

以大跨黄土隧道下穿公路安全施工为背景,对隧道下穿公路的安全施工方案进行研究。基于公路路面破损指数与下穿公路施工风险事件引起路面最大沉降之间的关系确定了隧道下穿施工可能引起的路面最大允许沉降量,并据此制定出施工管理基准,对比分析了CRD和CD法引起的隧道拱顶沉降、地表最大沉降、支护受力和隧道周边地层塑性区特征,建议采用CD法进行下穿施工。下穿孙辛路施工监测结果表明,采用CD法保证了隧道施工安全和孙辛路的正常通行。     

大型音乐舞蹈史诗《中国革命之歌》的艺术处理

大型音乐舞蹈史诗《中国革命之歌》在进行创作时既要确保艺术创作真实反映历史事实,又要防止与《东方红》重复,需要创作人员精心设计框架,选择材料进行加工改编,具有一定的难度。创作者和表演者通过艺术框架的搭建、艺术素材的加工、艺术演出的处理,使大型音乐舞蹈史诗《中国革命之歌》既具有政治内容又具有极高的艺术美。     

Empirical Likelihood for the Additive Hazards Model with Current Status Data

We investigate empirical likelihood for the additive hazards model with current status data. An empirical log-likelihood ratio for a vector or subvector of regression parameters is defined and its limiting distribution is shown to be a standard chi-squared distribution. The proposed inference procedure enables us to make empirical likelihood-based inference for the regression parameters. Finite sample performance of the proposed method is assessed in simulation studies to compare with that of a normal approximation method, it shows that the empirical likelihood method provides more accurate inference than the normal approximation method. A real data example is used for illustration.     

An Automatic Test for the Umbrella Alternatives

The paper proposes a new test for detecting the umbrella pattern under a general non‐parametric scheme. The alternative asserts that the umbrella ordering holds while the hypothesis is its complement. The main focus is put on controlling the power function of the test outside the alternative. As a result, the asymptotic error of the first kind of the constructed solution is smaller than or equal to the fixed significance level α on the whole set where the umbrella ordering does not hold. Also, under finite sample sizes, this error is controlled to a satisfactory extent. A simulation study shows, among other things, that the new test improves upon the solution widely recommended in the literature of the subject. A routine, written in R, is attached as the Supporting Information file.     

基于自组织的大型建筑企业控制力协同进化研究

针对大型建筑企业控制力动态协同的定量化仿真问题,基于复杂系统视角,应用自组织理论分析大型建筑企业控制力自组织耦合网络作用关系,选择有效朗之万方程构建大型建筑企业控制力系统的自组织协同进化模型,通过线性近似法的性态稳定求解非线性方程的稳定性,得出大型建筑企业控制力系统协同进化演化过程的四个决定性参数,并通过MATLAB软件进行参数枚举取值,具体分析企业控制力协同演化。案例验证该模型可对大型建筑企业控制力协同演化最佳状态实现更加精确的参数取值,并发现大型建筑企业控制力协同演化最佳状态的充要条件,以及一种新的大型建筑企业控制力协同演化状态。