L~2空间中的均方随机积分

本文在Ｌ￣２（ｄｕ）空间中定义了比Ｒｉｃｍａｎｎ均方积分更为广泛的一种均方随机积分，并讨论了这种积分的性质及随机积分可交换顺序定理。     

结构非线性风振的路径积分方法

通过引入相关脉动风速滤波,将结构非线性风振方程转变为Ito随机微分方程的形式;该方程的解过程具有Markov性质．在时域内将状态方程展开,利用其瞬时线性化随机方程的解析解,基于路径积分给出了结构非线性风振响应概率密度的形式解,得到了一种分析结构非线性风振响应的新方法．对桅杆算例的数值分析表明,该方法较线性频域分析方法和非线性时域积分方法具有更好的准确性和有效性．     

随机Volterra积分方程的非标准及演解法

本文借助星型Ｍｏｂｉｕｓ反演得到随机积分Ｖｏｌｔｅｒｒａ方程的一个全新解法．它旨在揭示离散反演与连续反演的内在联系，为探索各类反演的统一性提供了一种可能的研究途径．     

L2空间中的均方随机积分

本文在Ｌ²（ｄｕ）空间中定义了比Ｒｉｃｍａｎｎ均方积分更为广泛的一种均方随机积分，并讨论了这种积分的性质及随机积分可交换顺序定理。     

G可积函数的Lebesgue可测性

Botsko在连续和可导的知识基础上推广了Riemann积分,得到了一种新的积分,称为G积分．G积分既不同于Riemann积分也不同于Lebesgue积分．本文通过对G积分的研究,得到了G可积函数一定Lebesgue可测,从而有界G可积函数一定Lebesgue可积;同时我们还证明了这两个积分值相等．     

一个求总极值的实现算法及其收敛性

1978年,郑权等首先提出了一种用积分─水平集求总极值的方法及用Monte－Carlo随机投点实现的实现其法,其实现算法是否收敛未解决的问题．本文提出一种用数论方法实现的实现算法,并证明了该实现其法是收敛的．初步的数值结果表明,该实现其法是较有效的．     

利用二重积分解定积分问题

通过实例介绍如何用二重积分计算某些特殊的定积分．为定积分的计算提供一种思路,展示了二重积分与定积分在一定程度上的内在联系．     

B-积分的Denjoy型定义

该文在Rπ空间中定义了一种Denjoy型非绝对积分,证明了这种Denjoy型积分与B-积分等价,从而给出了B-积分的Denjoy形式．     

变测度的积分型全局优化算法

郑权等首先提出积分-水平集求总极值的方法,实现算法中采用Monte-Carlo 随机投点产生近似水平集来缩小搜索区域范围,但这一算法可能失去总极值点．此后,邬 冬华等给出了一种修正的积分－水平集的方法,一种区域不收缩的分箱方法以保证总极 值点不被丢失．本文在此基础上采取对不同的箱子采用不同的测度这一策略,使水平值 更充分的下降,更快的达到全局极小值,以提高修正算法的计算效率．最后给出的数值算 例说明了算法是有效的．     

一类积分不等式的规范化证法

本文利用定积分的线性变换,给出了一类积分不等式的一种规范化的证明方法．     

Stochastic dominance: A bibliographical rectification and a restatement of whitmore's theorem

The aim of this note is to make clear that the fundamental theorem on stochastic dominance of degree two was discovered in 1932 by Karamata. Apart from this historical rectification, it is interesting to remark that the proof is simple and elegant and can be used to characterize stochastic dominance of any order. We give a simple proof along these lines of Whitmore's theorem about third degree stochastic dominance.     

Stochastic uniform observability of linear differential equations with multiplicative noise

The aim of this paper is to give a deterministic characterization of the uniform observability property of linear differential equations with multiplicative white noise in infinite dimensions. We also investigate the properties of a class of perturbed evolution operators and we used these properties to give a new representation of the covariance operators associated to the mild solutions of the investigated stochastic differential equations. The obtained results play an important role in obtaining necessary and sufficient conditions for the stochastic uniform observability property.     

Uniform exponential dichotomy of stochastic cocycles

The aim of this paper is to give a generalization of the well-known theorem of Perron for uniform exponential dichotomy in mean square for stochastic cocycles in Hilbert spaces.     

Wong-Zakai approximations for stochastic differential equations

The aim of this paper is to give a wide introduction to approximation concepts in the theory of stochastic differential equations. The paper is principally concerned with Zong-Zakai approximations. Our aim is to fill a gap in the literature caused by the complete lack of monographs on such approximation methods for stochastic differential equations; this will be the objective of the author's forthcoming book. First, we briefly review the currently-known approximation results for finite- and infinite-dimensional equations. Then the author's results are preceded by the introduction of two new forms of correction terms in infinite dimensions appearing in the Wong-Zakai approximations. Finally, these results are divided into four parts: for stochastic delay equations, for semilinear and nonlinear stochastic equations in abstract spaces, and for the Navier-Stokes equations. We emphasize in this paper results rather than proofs. Some applications are indicated.The author's research was partially supported by KBN grant No. 2 P301 052 03.     

The Improved LaSalle-Type Theorems for Stochastic Differential Delay Equations

The main aim of this article is to deal with the almost-sure stability of stochastic differential delay equations. Our improved theorems give better results while conditions imposed on the Lyapunov function are much weaker, thus, it is easier to find a right Lyapunov function in application.     

The improved LaSalle-type theorems for stochastic functional differential equations

The main aim of this paper is to improve some results obtained by Mao [X. Mao, The LaSalle-type theorems for stochastic functional differential equations, Nonlinear Stud. 7 (2000) 307-328]. Our new theorems give better results while conditions imposed are much weaker than in the paper mentioned above. For example, we need only the local Lipschitz condition but neither the linear growth condition nor the bounded moment condition on the solutions. To guarantee the existence and uniqueness of the global solution to the underlying stochastic functional differential equation (SFDE) under the weaker conditions imposed in this paper, we establish a generalised existence-and-uniqueness theorem which covers a wider class of nonlinear SFDEs as demonstrated by the examples discussed in this paper. Moreover, from our improved results follow some new criteria on the stochastic asymptotic stability for SFDEs.     

Distributed Stochastic Algorithm for Global Optimization in Networked System

This paper studies the distributed optimization problem, whose aim is to find the global minimizer of the sum of multiple agents’ local nonconvex objective functions in a networked system. To solve such a distributed global optimization problem, we propose a distributed stochastic algorithm and we give detailed analysis of the global convergence of the proposed algorithm.     

随机赋范空间算子随机范数与Hahn-Banach延拓定理

基于概率测度理论基础,研究了随机赋范空间中算子随机范数,得到了线性算子空间与线性泛函的若干随机化结果与随机化的Hahn-Banach延拓定理.结果可能成为随机泛函分析与概率论及应用的理论工具.     

连续型随机变量的函数还是连续型随机变量吗？

本文研究了随机需求下随机利润的分布类型，给出了随机需求为连续型随机变量时，随机利润为连续型随机变量的充分必要条件，生动而有趣地回答了本文提出的问题。