A sharp inequality for martingales and its applications

In this paper, the best constant with respect to an inequality for martingales in Hall and Heyde (1980) is obtained. As a consequence, some large deviations with martingale difference and moving average process are established.     

The stability of neutral stochastic delay differential equations with Poisson jumps by fixed points

In the paper, the asymptotic mean square stability of the zero solution for neutral stochastic delay differential equations with Poisson jumps is studied by fixed points theory without Lyapunov functions. The coefficient functions have not been asked for a fixed sign, and the sufficient condition for mean square stability has been obtained. Therefore, some well-known results are improved and generalized.     

均值已知的条件下方差的统计推断

充分利用总体的信息，讨论了正态总体均值μ已知的条件下，方差σ^2的统计推断问题．     

PERIODIC SOLUTION FOR p-LAPLACIAN DIFFERENTIAL EQUATION WITH A DEVIATING ARGUMENT

By using the theory of coincidence degree, we study a kind of periodic solution to p-Laplacian differential equation with a deviating argument such as ((?)p(x'(t)))' f(x(t)) g(x(t - r(t))) = e(t), a result on the existence of periodic solution is obtained.     

Allocative efficiency of technically inefficient production units

We discuss how to measure allocative efficiency without presuming technical efficiency. This is relevant when it is easier to introduce reallocations than improvements of technical efficiency. We compare the approach to the traditional one of assuming technical efficiency before measuring allocative efficiency. In particular, we develop necessary and sufficient conditions in the technology to ensure consistent measures, we suggest alternative interpretations of the approaches, and we relate them to motivational and organizational change perspectives.     

Confidence sets and confidence bands for a beta distribution with applications to credit risk management

Incorporating statistical multiple comparisons techniques with credit risk measurement, a new methodology is proposed to construct exact confidence sets and exact confidence bands for a beta distribution. This involves simultaneous inference on the two parameters of the beta distribution, based upon the inversion of Kolmogorov tests. Some monotonicity properties of the distribution function of the beta distribution are established which enable the derivation of an efficient algorithm for the implementation of the procedure. The methodology has important applications to financial risk management. Specifically, the analysis of loss given default (LGD) data are often modeled with a beta distribution. This new approach properly addresses model risk caused by inadequate sample sizes of LGD data, and can be used in conjunction with the standard recommendations provided by regulators to provide enhanced and more informative analyses.     

有缺失数据的条件独立正态母体中参数的最优同变估计

在缺失数据机制是可忽略的假设下,导出了有单调缺失数据的条件独立正态模型中协方差阵和精度阵的Cholesky分解的最大似然估计和无偏估计.通过引入一类特殊的变换群并在更广义的损失下,获得了其最优同变估计.这表明最大似然估计和无偏估计是非容许的.最后,通过数值模拟验证了相关结果的有效性.     

Moderate deviations for neutral functional stochastic differential equations driven by Levy noises

Using the weak convergence method introduced by A. Budhiraja, P. Dupuis, and A. Ganguly [Ann. Probab., 2016, 44: 1723{1775], we establish the moderate deviation principle for neutral functional stochastic differential equations driven by both Brownian motions and Poisson random measures.