A Stochastic Tikhonov Theorem in Infinite Dimensions

The present paper studies the problem of singular perturbation in the infinite-dimensional framework and gives a Hilbert-space-valued stochastic version of the Tikhonov theorem. We consider a nonlinear system of Hilbert-space-valued equations for a "slow" and a "fast" variable; the system is strongly coupled and driven by linear unbounded operators generating a C₀-semigroup and independent cylindrical Brownian motions. Under well-established assumptions to guarantee the existence and uniqueness of mild solutions, we deduce the required stability of the system from a dissipativity condition on the drift of the fast variable. We avoid differentiability assumptions on the coefficients which would be unnatural in the infinite-dimensional framework.     

An Analog of the Sauer Theorem

In this paper, we present an analog of the Sauer theorem for projectively equivalent surfaces in the class of infinitely small equiareal deformations that pointwise preserve the spherical image of the surface.     

A THEOREM ON THE CONTINUITIES OF STOCHASTIC PROCESSES

If a stochastic process X_t is continuous in probability,then the points of discontinuityin γ-th mean constitute a set of lst category.     

Stochastic Local Gauss-Bonnet-Chern Theorem

The Gauss-Bonnet-Chern theorem for compact Riemannian manifold (without boundary) is discussed here to exhibit in a clear manner the role Riemannian Brownian motion plays in various probabilistic approaches to index theorems. The method with some modifications works also for the index theorem for the Dirac operator on the bundle of spinors, see Hsu.⁽⁷⁾     

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.     

A Strong Approximation Theorem for Stochastic Recursive Algorithms

The constant stepsize analog of Gelfand–Mitter type discrete-time stochastic recursive algorithms is shown to track an associated stochastic differential equation in the strong sense, i.e., with respect to an appropriate divergence measure.     

倒向随机微分方程解的比较定理

毛学荣新近将彭实戈和Ｐａｒｄｏｕｘ关于倒向随机策分方程解的存在性定理推广到非Ｌｉｐｓｃｈｉｔｚ系数情景,此文将彭实戈的比较定理推广到这一情形,主要工具是Ｔａｎａｋａ－Ｍｅｙｅｒ公式,Ｄａｖｉｓ不等式和Ｂｉｈａｒｉ不等式。     

Ito型随机积分方程依参数收敛性定理

本文在一定假设条件下，给出了一类　型随机积分方程依参数收敛性问题的一个定理，推广了［２］［３］的相应结果。     

Second Order Stochastic Inclusion

Abstract

The purpose of the paper is to consider some stochastic control problems as a particular case of a more general theory, the stochastic inclusions theory. We discuss the existence of weak solutions to a stochastic inclusion of second order, driven by two general semimartingales. Finally we present some examples.     

LaSalle''''s Theorem for Stochastic Differential Equations

In this paper, we establish a the LaSalle's theorem for stochastic differential equation based on Li's work, and give a more general Lyapunov function which it is more easy to apply. Our work has partly generalized Mao's work.     

随机微分方程LaSalle定理

In this paper, we establish a the LaSalle's theorem for stochastic differential equation based on Li's work, and give a more general Lyapunov function which it is more easy to apply. Our work has partly generalized Mao's work.     

A Birkhoff Theorem for Doubly Stochastic Matrices with Vector Entries

The concept of a doubly stochastic matrix whose entries come from a convex subset of the unit square is defined. It is proved that the only convex subsets of the unit square which contain (0,0) and (1, 1) and allow an extension of Birkhoff's characterization of the extreme points of the set of doubly stochastic matrices are parallelograms. A sufficient condition is given for a matrix to be extreme when the convex subset is not a parallelogram.     

关于积分第二中值定理改进的一个注记

对于积分第二中值定理的一种形式进行了进一步的讨论,从两个角度对于积分第二中值定理的结论进行了改进,给出了定理结论中的中值点ξ所属区间能强化为开区间的充要条件.     

代数体函数第二基本定理的推广

把代数体函数第二基本定理推广到了p个次数不超过d的多项式的情形,得到了类似于亚纯函数理论中Dufresnoy J推出的结果.     

代数体函数第二基本定理的一个推广

利用亚纯函数的Nevanlinna值分布理论,研究代数体函数第二基本定理的扩展形式,将该定理推广到两列互异且次数不超过d的多项式的情况,拓展了熊庆来、MillouX H等人的结果.     

An Analog of the Baer-Suzuki Theorem for Infinite Groups

We consider a group without infinite ascending chains of nilpotent subgroups and prove that if every two elements of some conjugacy class generates a nilpotent subgroup then the whole class also generates a nilpotent subgroup.