Non-Uniform in Time Robust Global Asymptotic Output Stability for Discrete-Time Systems

Existence of non-coercive Lyapunov functions is equivalent to integral uniform global asymptotic stability

In this paper, a class of abstract dynamical systems is considered which encompasses a wide range of nonlinear finite- and infinite-dimensional systems. We show that the existence of a non-coercive Lyapunov function without any further requirements on the flow of the forward complete system ensures an integral version of uniform global asymptotic stability. We prove that also the converse statement holds without any further requirements on regularity of the system. Furthermore, we give a characterization of uniform global asymptotic stability in terms of the integral stability properties and a…

Asymptotics of the optimum in discrete sequential assignment

We consider the stochastic sequential assignment problem of Derman, Lieberman and Ross (1972) corresponding to a discrete distribution supported on a finite set of points. We use large deviation estimates to compute the asymptotics of the optimal policy as the number of tasks $N \to \infty$.

On asymptotic optimality of Merton's myopic portfolio strategies for discrete time market

This paper studies the properties of discrete time stochastic optimal control problems associated with portfolio selection. We investigate if optimal continuous time strategies can be used effectively for a discrete time market after a straightforward discretization. We found that Merton's strategy approximates the performance of the optimal strategy in a discrete time model with the sufficiently small time steps

带有AMIS的SAA的一致指数收敛性及其最优值的渐近性

Uniform exponential convergence of SAA with AMIS and asymptotics of its optimal value

本文研究了带有自适应多重重要性采样的样本平均近似的一致指数收敛性及最优值渐近性，利用有界鞅差集中不等式获得新指数收敛速率，并基于泛函中心极限定理与Delta定理证明最优值渐近性。

Convergence of an inverse problem for discrete wave equations

It is by now well-known that one can recover a potential in the wave equation from the knowledge of the initial waves, the boundary data and the flux on a part of the boundary satisfying the Gamma-conditions of J.-L. Lions. We are interested in proving that trying to fit the discrete fluxes, given by discrete approximations of the wave equation, with the continuous one, one recovers, at the limit, the potential of the continuous model. In order to do that, we shall develop a Lax-type argument, usually used for convergence results of numerical schemes, which states that consistency and uniform …