A variational problem determined by probability measures

ABSTRACT

An optimization problem of maximizing an integral of a function over a family of probability measures is considered. The problem is a generalization of a well-studied variational problem in mathematical economics, concerning optimal allocations. The specific generalization that we examine arises also in the limit of singularly perturbed optimal control problems. We examine the mathematical problem and allude to the singular perturbation motivation.     

A note on random walks with absorbing barriers and sequential Monte Carlo methods

In this article, we consider importance sampling (IS) and sequential Monte Carlo (SMC) methods in the context of one-dimensional random walks with absorbing barriers. In particular, we develop a very precise variance analysis for several IS and SMC procedures. We take advantage of some explicit spectral formulae available for these models to derive sharp and explicit estimates; this provides stability properties of the associated normalized Feynman–Kac semigroups. Our analysis allows one to compare the variance of SMC and IS techniques for these models. The work in this article is one of the few to consider an in-depth analysis of an SMC method for a particular model-type as well as variance comparison of SMC algorithms.     

Stability criteria in terms of two measures for functional differential equation with variable‐time impulses

This paper focuses on the stability in terms of two measures for functional differential equation with variable‐time impulses. Being different from most of existing literatures, the impulses of functional differential equation are assumed to be closely associated to the current state. We propose a new comparison principle for the considered systems and establish several stability criteria in terms of two measures. Also, the theoretical results are applied in a class of delayed neural network systems with variable‐tine impulses, and numerical simulations are introduced to illustrate the effectiveness of our results. Copyright © 2014 John Wiley & Sons, Ltd.     

新课标体系下高师本科数学分析教学所面临的问题和所采取的措施

从三个方面讨论了在高中新课标体系下高师本科数学分析教学所面临的问题,并结合作者的实际教学经验给出了一些具有实际操作意义的解决措施和办法.     

重金属污染土壤植物修复的强化措施研究进展

植物修复是一种有着巨大市场潜力的治理重金属污染土壤的技术,由于影响植物修复效率的因素较多,至今实际应用还很少。针对目前植物修复技术的不足,主要从植物本身的性能、重金属的生物有效性以及农艺管理措施等三方面,综述了近年来国内外有关植物修复强化措施的研究进展,并展望了今后该领域的研究方向。     

Non-anticipative representations of Banach space valued gaussian processes with respect to brownian motion

Necessary and sufficient conditions are found for the equivalence of the measures associated with (i) a Banach space valued Gaussian process, with mean 0, and (ii) a Bach space valued Brownian motion. The notion of a non-anticipative representation of (i) with respect to (ii) is defined and in the case of equivalence of the measures it is shown that such a representation exists and has an explicit stochastic integral form which is invertible. Theorems of Ershov on absolute continuity of measures associated with diffusion processes are extended to Banach space. Applications to infinite-dimensional filtering are considered.     

Young measures generated by a class of integrands: a narrow epicontinuity and applications to Homogenization

Given a subset E of convex functions from into which satisfy growth conditions of order p>1 and an open bounded subset of , we establish the continuity of a map μΦ_μ from the set of all Young measures on equipped with the narrow topology into a set of suitable functionals defined in and equipped with the topology of Γ-convergence. Some applications are given in the setting of periodic and stochastic homogenization.