THE PATHWISE SOLUTION FOR A CLASS OF QUASILINEAR STOCHASTIC EQUATIONS OF EVOLUTION IN BANACH SPACE Ⅱ

ＴＨＥＰＡＴＨＷＩＳＥＳＯＬＵＴＩＯＮＦＯＲＡＣＬＡＳＳＯＦＱＵＡＳＩＬＩＮＥＡＲＳＴＯＣＨＡＳＴＩＣＥＱＵＡＴＩＯＮＳＯＦＥＶＯＬＵＴＩＯＮＩＮ　ＢＡＮＡＣＨＳＰＡＣＥⅡＨｕＹａｏｚｈｏｎｇ（ＷｕｈａｎＩｎｓｔ．ｏｆＭａｔｈ．Ｓｃｉ．，Ｃｈｉｎ．Ａ...     

ON THE EXISTENCE AND UNIQUENESS THEOREMS OF SOLUTIONS FOR A CLASS OF THE SYSTEMS OF MIXED MONOTONE OPERATOR EQUATIONS WITH APPLICATION

ＯＮＴＨＥＥＸＩＳＴＥＮＣＥＡＮＤＵＮＩＱＵＥＮＥＳＳＴＨＥＯＲＥＭＳＯＦＳＯＬＵＴＩＯＮＳＦＯＲＡＣＬＡＳＳＯＦＴＨＥＳＹＳＴＥＭＳＯＦＭＩＸＥＤＭＯＮＯＴＯＮＥＯＰＥＲＡＴＯＲＥＱＵＡＴＩＯＮＳＷＩＴＨＡＰＰＬＩＣＡＴＩＯＮＳＨＥＮＰＥＩＬＯＮＧ...     

THE NON－EXISTENCE OF PERIODIC SOLUTIONS OF A CERTAIN CLASS OF N－TH ORDER DIFFERENTIAL EQUATIONS

ＴＨＥ　ＮＯＮ－ＥＸＩＳＴＥＮＣＥ　ＯＦ　ＰＥＲＩＯＤＩＣ　ＳＯＬＵＴＩＯＮＳ　ＯＦ　Ａ　ＣＥＲＴＡＩＮ　ＣＬＡＳＳ　ＯＦ　Ｎ－ＴＨ　ＯＲＤＥＲ　ＤＩＦＦＥＲＥＮＴＩＡＬ　ＥＱＵＡＴＩＯＮＳＴＨＥＮＯＮ－ＥＸＩＳＴＥＮＣＥＯＦＰＥＲＩＯＤＩＣＳＯＬＵ...     

THE SOLUTION OF _b－EQUATION OF （P，Q）－FORMS AND IT＇S L~P＆HOLDER ESTIMATES ON A STEIN MANIFOLD

ＴＨＥＳＯＬＵＴＩＯＮＯＦ_ｂ－ＥＱＵＡＴＩＯＮＯＦ（Ｐ，Ｑ）－ＦＯＲＭＳＡＮＤＩＴ＇ＳＬ￣Ｐ＆ＨＯＬＤＥＲＥＳＴＩＭＡＴＥＳＯＮＡＳＴＥＩＮＭＡＮＩＦＯＬＤ￥ＷｕＸｉａｏｑｉｎ（ＤｅｐｔｏｆＭａｔｈ，ＪｉｍｅｉＴｅａｃｈｅｒｓＣｏｌｌｅｇｅＸｉａ?..     

THE UNIQUENESS AND CONTINUOUS DEPENDENCE FOR CHARACTERISTIC CAUCHY PROBLEM OF PARTIAL DIFFERENTIAL EQUATIONS

ＴＨＥＵＮＩＱＵＥＮＥＳＳＡＮＤＣＯＮＴＩＮＵＯＵＳＤＥＰＥＮＤＥＮＣＥＦＯＲＣＨＡＲＡＣＴＥＲＩＳＴＩＣＣＡＵＣＨＹＰＲＯＢＬＥＭＯＦＰＡＲＴＩＡＬＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＬｕａｎＷｅｎｇｕｉ（栾文贵）（ＣｏｍｐｕｔｉｎｇＣｅｎｔ...     

A NOTE FOR THE TOPOLOGICAL CLASSIFICATION OF STRUCTURALLY STABLE QUADRATIC DIFFERENTIAL SYSTEMS WITHOUT LIMIT CYCLES

ＡＮＯＴＥＦＯＲＴＨＥＴＯＰＯＬＯＧＩＣＡＬＣＬＡＳＳＩＦＩＣＡＴＩＯＮＯＦＳＴＲＵＣＴＵＲＡＬＬＹＳＴＡＢＬＥＱＵＡＤＲＡＴＩＣＤＩＦＦＥＲＥＮＴＩＡＬＳＹＳＴＥＭＳＷＩＴＨＯＵＴＬＩＭＩＴＣＹＣＬＥＳ￥ＹｅＷｅｉｙｉｎ（叶惟寅）（ＮａｎｊｉｎｇＮ...     

POSITIVE SOLUTIONS AND BIFURCATION OF FULLY NONLINEAR ELLIPTIC EQUATIONS INVOLVING SUPER－CRITICAL SOBOLEV EXPONENTS

ＰＯＳＩＴＩＶＥＳＯＬＵＴＩＯＮＳＡＮＤＢＩＦＵＲＣＡＴＩＯＮＯＦＦＵＬＬＹＮＯＮＬＩＮＥＡＲＥＬＬＩＰＴＩＣＥＱＵＡＴＩＯＮＳＩＮＶＯＬＶＩＮＧＳＵＰＥＲ－ＣＲＩＴＩＣＡＬＳＯＢＯＬＥＶＥＸＰＯＮＥＮＴＳ￥ＱＵＣＨＡＮＧＺＨＥＮＧ（屈长征）（Ｉｎｓ...     

THE EXISTENCE OF A WEAK SOLUTION OF QUASILINEAR ELLIPTIC EQUATION WITH CRITICAL SOBOLV EXPONENT ON UNBOUNDED DOMAIN

ＴＨＥＥＸＩＳＴＥＮＣＥＯＦＡＷＥＡＫＳＯＬＵＴＩＯＮＯＦＱＵＡＳＩＬＩＮＥＡＲＥＬＬＩＰＴＩＣＥＱＵＡＴＩＯＮＷＩＴＨＣＲＩＴＩＣＡＬＳＯＢＯＬＶＥＸＰＯＮＥＮＴＯＮＵＮＢＯＵＮＤＥＤＤＯＭＡＩＮＬｉＧｏｎｇｂａｏ（李工宝）（Ｉｎｓｔ．ｏｆＭａｔｈ...     

A CLASS OF FACTORIZATION UPDATE ALGORITHM FOR SOLVING SYSTEMS OF SPARSE NONLINEAR EQUATIONS

ＡＣＬＡＳＳＯＦＦＡＣＴＯＲＩＺＡＴＩＯＮＵＰＤＡＴＥＡＬＧＯＲＩＴＨＭＦＯＲＳＯＬＶＩＮＧＳＹＳＴＥＭＳＯＦＳＰＡＲＳＥＮＯＮＬＩＮＥＡＲＥＱＵＡＴＩＯＮＳＢＡＩＺＨＯＮＧＺＨＩ（ＩｎｓｔｉｔｕｔｅｏｆＣｏｍｐｕｔａｔｉｏｎａｌＭａｔｈｅｍａｔｉｃ...     

NONNULL DISTRIBUTION OF THE LIKELIHOOD RATIO CRITERION FOR TESTING THE EQUALITY OF DIAGONAL BLOCKS WITH BLOCKWISE INDEPENDENCE

ＮＯＮＮＵＬＬＤＩＳＴＲＩＢＵＴＩＯＮＯＦＴＨＥＬＩＫＥＬＩＨＯＯＤＲＡＴＩＯＣＲＩＴＥＲＩＯＮＦＯＲＴＥＳＴＩＮＧＴＨＥＥＱＵＡＬＩＴＹＯＦＤＩＡＧＯＮＡＬＢＬＯＣＫＳＷＩＴＨＢＬＯＣＫＷＩＳＥＩＮＤＥＰＥＮＤＥＮＣＥＡ．Ｋ．Ｇｕｐｔａ；Ｃ．Ｃ．Ｃ...     

The characterization of certain quantum stochastic stationary process

In this paper we will obtain a Stone type theorem under the frame of Hilbert C＊-module, such that the classical Stone theorem is our special case. Then we use it as a main tool to obtain a spectrum decomposition theorem of certain stationary quantum stochastic process. In the end, we will give it an interpretation in statistical mechanics of multi-linear response.     

Stochastic viscosity solutions for nonlinear stochastic partial differential equations. Part II

This paper is a continuation of our previous work (Part I, Stochastic Process. Appl. 93 (2001) 181–204), with the main purpose of establishing the uniqueness of the stochastic viscosity solution introduced there. We shall prove a comparison theorem between a stochastic viscosity solution and an ω-wise stochastic viscosity solution, which will lead to the uniqueness results. As the byproducts we extend the measurable section theorem of Dellacherie and Meyer (1978), and a fundamental lemma of Crandall et al. (1992)     

The substitution theorem for semilinear stochastic partial differential equations

In this article we establish a substitution theorem for semilinear stochastic evolution equations (see's) depending on the initial condition as an infinite-dimensional parameter. Due to the infinite-dimensionality of the initial conditions and of the stochastic dynamics, existing finite-dimensional results do not apply. The substitution theorem is proved using Malliavin calculus techniques together with new estimates on the underlying stochastic semiflow. Applications of the theorem include dynamic characterizations of solutions of stochastic partial differential equations (spde's) with anticipating initial conditions and non-ergodic stationary solutions. In particular, our result gives a new existence theorem for solutions of semilinear Stratonovich spde's with anticipating initial conditions.     

关于任意随机适应序列部分和增长阶的估计

设(Ω,F,P)为概率空间,{Xn,Fn,n 0}为定义在上面的随机适应序列.目的是要研究任意随机适应序列的一个强极限定理.作为推论,推广了Freedman的一个定理以及任意随机适应序列部分和增长阶估计定理.     

Weak Characterizations of Stochastic Integrability and Dudley’s Theorem in Infinite Dimensions

In this paper we consider stochastic integration with respect to cylindrical Brownian motion in infinite-dimensional spaces. We study weak characterizations of stochastic integrability and present a natural continuation of results of van Neerven, Weis and the second named author. The limitation of weak characterizations will be demonstrated with a nontrivial counterexample. The second subject treated in the paper addresses representation theory for random variables in terms of stochastic integrals. In particular, we provide an infinite-dimensional version of Dudley’s representation theorem for random variables and an extension of Doob’s representation for martingales.     

任意随机组列的强极限定理

本文研究了任意随机组列的极限性质.利用构造鞅的方法得到了任意随机组列的强极限定理,所得结果摊广了任意随机适应序列和树上非齐次马氏链的强极限定理.     

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.     

Stochastic integral with respect to set-valued square integrable martingales

In this paper, we shall firstly illustrate why we should consider integral of a stochastic process with respect to a set-valued square integrable martingale. Secondly, we shall prove the representation theorem of set-valued square integrable martingale. Thirdly, we shall give the definition of stochastic integral of a stochastic process with respect to a set-valued square integrable martingale and the representation theorem of this kind of integrals. Finally, we shall prove that the stochastic integral is a set-valued sub-martingale.     

Stochastic Convolution-Type Heat Equations with Nonlinear Drift

Abstract

In this article, we study the solution of a class of stochastic convolution-type heat equations with nonlinear drift. For general initial condition and coefficients, we prove existence and uniqueness by using the characterization theorem and Banach's fixed-point theorem. We also give an implicit solution, which is a well-defined generalized stochastic process in a suitable distribution space. Finally, we investigate the continuous dependence of the solution on the initial data as well as the dependence on the coefficient.     

Boundary Value Problems for First Order Stochastic Differential Equations

In this paper, we present a new technique to study nonlinear stochastic differential equations with periodic boundary value condition （in the sense of expectation）. Our main idea is to decompose the stochastic process into a deterministic term and a new stochastic term with zero mean value. Then by using the contraction mapping principle and Leray-Schauder fixed point theorem, we obtain the existence theorem. Finally, we explain our main results by an elementary example.