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学 术 报 告报告人：戴民教授（新加坡国立大学）题目：Asymptotic for Merton problem with capital gain tax and small interest rate时间：2014年12月11日，星期四下午4：00—5：00地点：数学系致远楼107欢迎各位参加

We develop a constructive approach to estimating a sparse linear regression model in high-dimensions. The proposed approach is a computational algorithm that generates a sequence of solutions iteratively, based on support detection using primal and dual information and root finding according to a modified KKT condition for the L0-penalized least squares criterion. We refer to the proposed algorithm as SDAR for brevity. Under certain regularity conditions on the design matrix and sparsity assumption on the regression coefficients, we show that with high probability, the errors of the solution sequence decay exponentially to the minimax error bounds in the Gaussian noise case. Moreover, with high probability, it takes no more than O(log(R)) steps to recover the oracle estimator, where R is the relative magnitude of the nonzero coefficients.

Treatment effect is an important index in comparing two-sample data in survival analysis, industry manufacture, clinical medicine and many other applications. In this paper, we propose a unified semiparametric approach to estimate different types of treatment effects under a case-control sampling plan with the logistic regression model assumption, which is equivalent to a two-sample density ratio model. For different treatment effects, we construct different estimating functions and the nuisance parameters in estimating functions are estimated firstly by the empirical likelihood method. Here, we allow that the functions are nonsmooth with respect to parameters. The confidence interval for the treatment effect based on the empirical likelihood ratio method is also presented. We prove that the estimator based on the estimating equation is consistent and asymptotically normal and the empirical log-likelihood ratio statistic has a limiting scaled chi-square distribution.

In this talk, we consider the modules for the Heisenberg-Virasoro algebra and the W-algebra W(2, 2). We determine the modules whose restriction to the Cartan subalgebra or maximal toral subalgebra (modulo center) are free of rank 1 for these two algebras. We also determine the simplicity of these modules. These modules provide new simple modules for the W-algebra W(2, 2).

学 术 报 告报 告 人： 王 宏 玉 教授（扬州大学数学学院）报告题目：From Kodaira Conjecture To Donaldson Question 报告时间：2014年12月4日（周四）下午16：00-17:00 报告地点：致远楼107室欢迎广大师生参加！ 2014-12-

学 术 报 告报 告 人： 郑 宇 教授（华东师范大学数学系）报告题目：Some New Study On Differential Hanarck Inequality Along Ricci Flow报告时间：2014年12月4日（周四）下午15：00-16:00报告地点：致远楼107室欢迎广大师生参加！ 2014-12-

On the convergence to stochastic integrals, most of previous works imposed a semi-martingale structure in establishing the asymptotics. This semi-martingale structure is not sufficiently general in many econometric applications, particularly in framework of cointegration. In this paper, we investigate the convergence to stochastic integrals beyond the semi-martingale. It is shown that limitation is essentially different if the semi-martingale innovation is replaced by a linear process or a sequence of mixing random variables, extending earlier results of Ibragimov and Phillips (2008) and De Jong (2002).

近年来大量的实验数据证实了噪音对复杂系统的动态特征有着重要影响。因此复杂系统的随机建模和随机模拟是今年来的研究热点之一。本报告首先针对随机微分方程和随机生化反应系统讨论随机系统的基本模拟方法和建模技巧。然后讨论如何针对金融学和生物学中复杂系统的数学建模。将着重讨论基因调控网络和细胞信号传导通道的随机建模。最后将介绍如何利用极大似然估计和贝叶斯方法对随机模型的未知参数进行估计