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The construction of Markov processes in random environments and the equivalence theorems

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Science china mathematics 2004年第4期47卷 481-496页

作者： HU DiheSchool of mathematics and Statistics, wuhan university, wuhan 43.072, china 1. School of mathematics and Statistics Wuhan University 430072 Wuhan China

In sec.1, we introduce several basic concepts such as random transition function, p-m process and Markov process in random environment and give some examples to construct a random transition function from a non-homogeneous density function. In sec.2, we construct the Markov process in random enviromment and skew product Markov process by p - m process and investigate the properties of Markov process in random environment and the original process and environment process and skew product process. In sec. 3, we give several equivalence theorems on Markov process in random environment.

关键词： radom transition function, p -m process, Markov process in random environment, skew product Markov process, density function.

LARGE DEVIATIONS FOR STATIONARY Φ-MIXING SEQUENCES IN τ-TOPOLOGY

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Chinese Annals of mathematics,Series B 1996年第2期17卷 149-158页

作者： Hu YIJUN Department of mathematics, wuhan university, wuhan 43.072, china. Department of mathematics Wuhan University Wuhan 430072 China

The results of Bryc on large deviations for empirical measures of stationary Φ-mixing sequences are extended. Bryc states his results in the usual weak topology on the space ofprobability measures. In this paper, under somewhat weaker assumptions than those of Bryc,the author extends Bryc's results by taking the finer topology which is generated by the integralsover bounded measurable functions.

关键词： Large deviation Empirical measure Stationary sequence Φ-mixing τ-topology

On the value distribution of Julia points

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Chinese Science Bulletin 1997年第22期42卷 1856-1857页

作者： SUN DaochunDepartment of mathematics, wuhan university, wuhan 43.072, china Department of mathematics Wuhan University Wuhan China

CONSIDER the rational fractional mapping R: V→V on the complex sphere V. We use themethod of the value distribution to study the properties near Julia points to understand Juliapoints.

关键词： complex dynamics Julia point value distribution.

Large deviation principles for stationary NA sequences

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Chinese Science Bulletin 1998年第7期43卷 536-540页

作者： HU Yijun Department of mathematics, wuhan university, wuhan 43.072, china Department of mathematics Wuhan University Wuhan China

Under general conditions, the large deviation principles for partial sums of stationary NA sequences are proved.

关键词： NA sequence stationary sequence partial sums large deviation principle.

DOUBLE Φ-FUNCTION INEQUALITY FOR NONNEGATIVE SUBMARTINGALES

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Chinese Annals of mathematics,Series B 2000年第2期21卷 211-216页

作者： MEI TAO(College of mathematics and Computer Sciences, wuhan university, wuhan 43.072, china.) LIU PEIDE(College of mathematics and Computer Sciences, wuhan university, wuhan 43.072, china.) College of mathematics and Computer Sciences Wuhan University Wuhan 430072 China

The authors establish a kind of inequalities for nonnegative submartingales which depend on two functions　ψ and ψ, and obtain the equivalent conditions for　Φ and ψ such that this kind of inequalities holds. In t... 详细信息

关键词： Matingale Nonnegative submartingale Maximal function Φ-function inequality

Atomic decomposition in L^p(R^n) (1

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Chinese Science Bulletin 1999年第24期44卷 2221-2225页

作者： YANG QixiangDepartment of mathematics , wuhan university , wuhan 43.072 , china Department of mathematics Wuhan University Wuhan China

An atomic decomposition in Lp (1 < p < 2) with tent space is given.

关键词： Lp s( n) tent space Tp5 q (p Tp5 q) atom (p L2) atom atomic decomposition.

Central limit theorem on noncompact Riemannian symmetric spaces of rank one

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Chinese Science Bulletin 1997年第15期42卷 1247-1250页

作者： ZHU FuliuDepartment of mathematics, wuhan university, wuhan 43.072, china Department of mathematics Wuhan University Wuhan China

IN 1994, Terras obtained the central limit theorem on Poincare upper half planeM=SL(2,R)/SO(2). This is the first non-Euclidean central limit theorem on a noncompactRiemannian symmetric space. Based on the spherical Follrier transform, using the expressionsof the heat kernel obtained by Lohoue et al. , we establish in this note the non-Euclideancentral limit theorem on noncompact Riemannian symmetric spaces of rank one.

关键词： Riemannian symmetric space central limit theorem.

The Fourier Transformations of Positive Distributions on Lorentz Group SO(3,1)

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wuhan university Journal of Natural Sciences 2001年第3期6卷 631-642页

作者： Zhu Li College of mathematics and Statistics, wuhan university, wuhan 43.072,china wuhan university College of Mathematics and Statistics Wuhan China (GRID:grid.49470.3e) (ISNI:***)

With the aid of Plancherel-Godement Theorem, we prove that every positive distributionT onSO (3, 1) which is bi-invariant underSO(3) corresponds to a measure μ on ω=∝σC|s(2-s)>=0∝, and μ can be decomposed intoμ... 详细信息

关键词： K-bi-in-invariant positive distribution spherical Fourier transformation Laplace-Beltrami operator

Smooth solutions of non-linear stochastic partial differential equations driven by multiplicative noises

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Science china mathematics 2010年第11期53卷 2949-2972页

作者： ZHANG XiCheng School of mathematics and Statistics, wuhan university, wuhan 43.072, china 1. School of mathematics and Statistics Wuhan University Wuhan 430072 China

In this paper, we study the regularity of solutions of nonlinear stochastic partial differential equations (SPDEs) with multiplicative noises in the framework of Hilbert scales. Then we apply our abstract result to several typical nonlinear SPDEs such as stochastic Burgers and Ginzburg-Landau equations on the real line, stochastic 2D Navier-Stokes equations (SNSEs) in the whole space and a stochastic tamed 3D Navier-Stokes equation in the whole space, and obtain the existence of their smooth solutions respectively. In particular, we also get the existence of local smooth solutions for 3D SNSEs.

关键词： smooth solutions stochastic partial differential equations stochastic Navier-Stokes equations