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A change point refers to a location or time at which observations or data obey two different models: before and after. These studies of change-point problems have found applications in a wide range of areas, including quality control, finance, environmetrics, medicine, genetics and geography. We propose a procedure for detecting multiple change-points in a mean-shift model. We first convert the change-point problem into a variable selection problem by partitioning the data sequence into several segments. Then, we apply a modified variance inflation factor regression algorithm to each segment in sequential order.

We study the Poisson-Nernst-Planck (PNP) system with an arbitrary number of ion species with arbitrary valences in the absence of fixed charges. Assuming point charges and that the Debye length is small relative to the domain size, we derive an asymptotic formula for the steady-state solution by matching outer and boundary layer solutions. The case of two ionic species has been extensively studied, the uniqueness of the solution has been proved, and an explicit expression for the solution has been obtained. However, the case of three or more ions has received significantly less attention.

Using the marked empirical processes, this paper develops a test of parametric specification in a nonlinear cointegrating regression model. Unlike the kernel-smoothed $U$-statistic considered in Gao, et al. (2009) and Wang and Phillips (2012), our new test statistic avoids the use of bandwidth, which has some advantages for practitioners. Simulations and a real data example show that our new test has a good finite sample performance. Another contribution of this paper is to provide a rigorous proof on weak convergence for a class of martingales, which is interesting in its own rights.

Stochastic multiscale modeling has become a popular approach to quantify uncertainty in multiscale models. The combination of multiscale features and complex uncertainty in models leads to great challenge to simulate the models and explore the propagation of uncertainty. To treat the difficulty, it is desirable to construct a sparse representation for the outputs of the multiscale models. In the talk, we present a sparse representation based on reduced multiscale basis methods and investigate uncertainty quantification for some porous media applications.

We consider the optimal dividend payment strategy for an insurance company, having two collaborating business lines, where their surplus processes are modelled by diffusion processes and the dividends paid by different business lines are weighted differently. We find the optimal dividend strategy when money is transferred between two business lines without transaction costs. We show the optimal value function is the unique continuous viscosity solution to the corresponding HJB equation when money is transferred with transaction costs. We also prove a verification theorem. Finally, we find the optimal solution to the problem with transaction costs in the symmetric case.

We consider the optimal investment and consumption decision of a CRRA investor who is facing capital gains tax and receives labor income. Assume that the investor cannot borrow against future labor income. We investigate how the coexistence of capital gains tax and uninsurable labor income affects the investment and consumption decision. This work is jointly with Yaoting Lei and Hong Liu

Due to the lack of separation principle, the problem of output feedback stabilization for nonlinear systems has been known as a challenging problem. This talk will sketch the recent efforts in solving this problem for several classes of nonlinear systems. The specific topics will cover: continuous-time output feedback control; finite-time output feedback control; sampled-data output feedback control; output feedback control of linearly uncontrollable systems; and applications to some practical systems. Dr. Chunjiang Qian received his B.S. and M.S degrees in Control Theory from Fudan University in 1992 and 1994 respectively, and the Ph.D. degree in Electrical Engineering from Case Western Reserve University, 2001. Since August 2001

Buffon投针是随机几何的一个经典范例。为了研究几何体的随机现象，几何元素集的测度是最基本的问题。本报告将介绍直线集等几何元素集的运动密度、经典等周不等式的Blaschke证明以及Poincaré公式、Blaschke运动基本公式等