关于任意离散随机序列的一个强偏差定理

引用极限对数似然比的概念作为任意随机序列联合分布与其边缘分布"不相似性"的度量,构造几乎处处收敛的上鞅,讨论了任意离散随机序列的强偏差定理.     

关于任意非负随机序列随机和的一类随机偏差定理

本文引入任意随机变量序列随机极限对数似然比概念,作为任意相依随机序列联合分布与其边缘乘积分布“不相似”性的一种度量,利用构造新的密度函数方法来建立几乎处处收敛的上鞅,在适当的条件下,给出了任意受控随机序列的一类随机偏差定理.     

关于任意随机可积序列的一个强收敛定理

本文研究了可积随机适应序列强收敛定理的问题.利用构造截尾停时以及鞅差序列的方法,获得了一类任意积随机适应序列的强收敛定理,推广了若干已知的结果.     

B值鞅差序列和的收敛速度

在随机元的尾概率随机有界的情况下,我们讨论了Ｂ值鞅差序列非随机足标与随机足标部分和的收敛速度,使得实值独立同分布随机变量序列的一些经典结果得到了推广和一般化,并且当０＜ｔ＜１时,我们证明了对任意Ｂ值随机元结论都是成立的．     

任意随机变量序列的一个强极限定理

研究任意随机变量序列的强收敛性.利用鞅差序列级数收敛定理,证明了任意随机序列的一个强极限定理,作为推论,得到了马氏过程、鞅差序列及独立随机变量序列的强大数定律.     

任意随机序列关于二重非齐次马氏链的随机和的一类随机选择系统的随机逼近定理

本文引进任意随机变量序列随机极限对数似然比的概念,通过测度$\pr$下任意相依随机序列联合分布与测度$\qr$下二重非齐次马氏分布相比较,利用母函数与尾概率母函数工具研究任意受控随机序列之随机和在随机选择系统中的一类随机逼近定理.     

任意随机序列级数的强收敛性

利用鞅差序列级数收敛定理研究任意随机序列级数的强收敛性,得到了该序列的一个强极限定理,某些经典的鞅差序列和独立随机变量序列的强极限定理是其特例.     

随机规划中的一些逼近结果

主要讨论了一类随机规划的目标函数分别在概率测度序列分布收敛、函数序列上图收敛以及随机变量序列均方可积收敛等收敛意义下目标函数序列的收敛情况。基于上述收敛情况给出了一些逼近思想，这些思想可应用于求解这类随机规划问题。     

随机Bernstein多项式的依分布收敛问题

利用随机的Bernstein多项式研究随机逼近问题具有一定的意义.借助弱收敛的概念,从分布函数的角度,讨论了随机Bernstein多项式依分布收敛问题.同时,与依概率收敛结果相比较,以此说明Bernstein多项式序列依分布收敛适用的范围更广.     

关于相依离散随机序列的若干强偏差定理

首次引入随机序列滑动似然比与滑动相对熵概念作为刻画任意相依随机序列的独立逼近的随机性度量,利用B-C引理与分析方法相结合,研究任意离散随机序列部分和滑动平均的强偏差定理.作为推论,得到了关于广义经验分布函数的一个极限定理.最后,给出了若干例子.     

On a class of stochastic differential equations arising from the stochastic approximation theory

The paper dealt with generalized stochastic approximation procedures of Robbins-Monro type. We consider these procedures as strong solutions of some stochastic differential equations with respect to semimartingales and investigate their almost sure convergence and mean square convergence     

Approximating Stationary Points of Stochastic Mathematical Programs with Equilibrium Constraints via Sample Averaging

We investigate sample average approximation of a general class of one-stage stochastic mathematical programs with equilibrium constraints. By using graphical convergence of unbounded set-valued mappings, we demonstrate almost sure convergence of a sequence of stationary points of sample average approximation problems to their true counterparts as the sample size increases. In particular we show the convergence of M(Mordukhovich)-stationary point and C(Clarke)-stationary point of the sample average approximation problem to those of the true problem. The research complements the existing work in the literature by considering a general constraint to be represented by a stochastic generalized equation and exploiting graphical convergence of coderivative mappings.     

A stochastic inertial forward–backward splitting algorithm for multivariate monotone inclusions

We propose an inertial forward–backward splitting algorithm to compute a zero of a sum of two monotone operators allowing for stochastic errors in the computation of the operators. More precisely, we establish almost sure convergence in real Hilbert spaces of the sequence of iterates to an optimal solution. Then, based on this analysis, we introduce two new classes of stochastic inertial primal–dual splitting methods for solving structured systems of composite monotone inclusions and prove their convergence. Our results extend to the stochastic and inertial setting various types of structured monotone inclusion problems and corresponding algorithmic solutions. Application to minimization problems is discussed.     

Numerical Solution of Stochastic Ito-Volterra Integral Equations Using Haar Wavelets

This paper presents a computational method for solving stochastic Ito-Volterra integral equations. First, Haar wavelets and their properties are employed to derive a general procedure for forming the stochastic operational matrix of Haar wavelets. Then, application of this stochastic operational matrix for solving stochastic Ito-Volterra integral equations is explained. The convergence and error analysis of the proposed method are investigated. Finally, the efficiency of the presented method is confirmed by some examples.     

随机微分方程欧拉格式算法分析

首先给出了线性随机微分方程的欧拉格式算法,然后给出了非线性随机微分方程变步长的欧拉格式算法,接着讨论了其对初值的连续依赖性和收敛性.     

离散随机序列随机和的一类强偏差定理

In this paper, the notion of limit random logarithmic likelihood ratio of stochastic se-quences,as a measure of “dissimilarity“ between their joint distributions and the product of theirmarginals,is introduced. Construct a. s. convergence supermartingale by means of truncation methodand under suitable restrict Chung-Teicher type conditions,some strong deviation theorems for arbi-trary discrete stochastic sequence are obtained.     

Continuous approximation schemes for stochastic programs

One of the main methods for solving stochastic programs is approximation by discretizing the probability distribution. However, discretization may lose differentiability of expectational functionals. The complexity of discrete approximation schemes also increases exponentially as the dimension of the random vector increases. On the other hand, stochastic methods can solve stochastic programs with larger dimensions but their convergence is in the sense of probability one. In this paper, we study the differentiability property of stochastic two-stage programs and discuss continuous approximation methods for stochastic programs. We present several ways to calculate and estimate this derivative. We then design several continuous approximation schemes and study their convergence behavior and implementation. The methods include several types of truncation approximation, lower dimensional approximation and limited basis approximation.His work is supported by Office of Naval Research Grant N0014-86-K-0628 and the National Science Foundation under Grant ECS-8815101 and DDM-9215921.His work is supported by the Australian Research Council.     

Runge–Kutta Methods for Itô Stochastic Differential Equations with Scalar Noise

A general class of stochastic Runge–Kutta methods for Itô stochastic differential equation systems w.r.t. a one-dimensional Wiener process is introduced. The colored rooted tree analysis is applied to derive conditions for the coefficients of the stochastic Runge–Kutta method assuring convergence in the weak sense with a prescribed order. Some coefficients for new stochastic Runge–Kutta schemes of order two are calculated explicitly and a simulation study reveals their good performance.     

Stochastic Programming with Equilibrium Constraints

In this paper, we discuss here-and-now type stochastic programs with equilibrium constraints. We give a general formulation of such problems and study their basic properties such as measurability and continuity of the corresponding integrand functions. We discuss also the consistency and rate of convergence of sample average approximations of such stochastic problems