Moderate Deviations for Bayes Posteriors

Let ( X_k ) k be a sequence of i.i.d. random variables taking values in a set , and consider the problem of estimating the law of X₁ in a Bayesian framework. We prove, under mild conditions on the prior, that the sequence of posterior distributions satisfies a moderate deviation principle.     

深水钻孔灌注桩基础施工技术

针对济阳黄河公路大桥钻孔灌注桩桩身长、孔壁易失稳垮塌、单桩混凝土灌注量大等施工难题，通过合理机械选型和控制护壁泥浆配比，取得了良好效果。以4″主墩为例介绍了施工条件及钻孔灌注桩施工技术措施，总结了施工效果。     

救赎：寻求民族文化的出路——解读莫里森的《柏油孩子》

高速铁路具有高度集成、高精度的技术特点，运营过程中经受列车质量、速度、密度等多种因素影响，地理位置因素往往是影响铁路设备状态演变的决定性因素。采用网格化管理技术可将空间上连续分布的管理对象划分成较小的单元网格，有利于从空间位置角度研究管理对象状态的变化规律。随着信息系统技术、大数据技术的迅猛发展，基于位置而不是基于专业更符合高速铁路的管理需求，网格化管理技术给高速铁路管理带来了新的视角。     

Conditional entropy,entropy density,and strong law of large numbers for generalized controlled tree-indexed Markov chains

In this paper, we first introduces a tree model without degree boundedness restriction namely generalized controlled tree T, which is an extension of some known tree models, such as homogeneous tree model, uniformly bounded degree tree model, controlled tree model, etc. Then some limit properties including strong law of large numbers for generalized controlled tree-indexed non homogeneous Markov chain are obtained. Finally, we establish some entropy density properties, monotonicity of conditional entropy, and entropy properties for generalized controlled tree-indexed Markov chains.     

The almost sure convergence rate of the estimator of optimized certainty equivalent risk measure under α-mixing sequences

Conditional value-at-risk (CVaR) model is a kind of financial risk measure that is extensively supported and accepted by international financial community. Its optimized form can be regarded as an optimized certainty equivalent (OCE) risk measurement. In this paper, we mainly discuss and analyze the strong laws of large numbers and the convergence rate of OCE's estimator under α-mixing sequences. The result shows that the almost sure convergence rate of CVaR estimator is given by the results of OCE estimator. Its convergence rate is inversely proportional to the square root of the sample size under certain conditions. Its effectiveness is verified by simulation experiments for two classical α-mixing sequences.     

Precise large deviations for the difference of two sums of END random variables with heavy tails

Assume that there are two types of insurance contracts in an insurance company, and the ith related claims are denoted by {X_ij, j ? 1}, i = 1, 2. In this article, the asymptotic behaviors of precise large deviations for non random difference ∑^n₁(t)_{j = 1}X_1j ? ∑^n₂(t)_{j = 1}X_2j and random difference ∑^N₁(t)_{j = 1}X_1j ? ∑^N₂(t)_{j = 1}X_2j are investigated, and under several assumptions, some corresponding asymptotic formulas are obtained.     

Hypothesis Testing in a Rayleigh Diffusion Model

Applying the large and moderate deviations for the log-likelihood ratio of the Rayleigh diffusion model, we give the negative regions in testing Rayleigh diffusion model and obtain the decay rates of the error probabilities.     

Complete convergence and the strong laws of large numbers for pairwise NQD random variables

The authors study the strong convergence for sequences of pairwise negatively quadrant dependent (NQD) random variables under some wide conditions, and present some new theorems on the complete convergence and the strong laws of large numbers. The obtained results extend and improve some theorems in existing literature.     

Strong law of large numbers and complete convergence for non-identically distributed WOD random variables

In this paper, we establish the strong law of large numbers and complete convergence for non-identically distributed WOD random variables. We derive some new inequalities of Fuk–Nagaev type for the sums of non-identically distributed WD random variables. All these results further extend and refine previous ones.     

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.