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Stochastic quantization and ergodic theorem for density of diffusions

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Science China Mathematics 2012年第11期55卷 2285-2296页

作者： HU YaoZhong Department of Mathematics University of Kansas Lawrence KS 66045 USA

For a given probability density function p（x） on R^d, we construct a （non-stationary） diffusion process xt, starting at any point x in R^d, such that 1/T ∫_o^T δ（xt-x）dt converges to p（x） almost surely. The rate of this convergence is also investigated. To find this rate, we mainly use the Clark-Ocone formula from Malliavin calculus and the Girsanov transformation technique.

关键词： Stochastic quantization diffusions Malliavan calculus ergodic theorem local time Clark-Oconeformula Girsanov formula Donsker delta functional heat kernel

ergodic theorem for the two-dimensional super-Brownian motion with super-Brownian immigration

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Progress in Natural Science:Materials International 2000年第2期 33-38页

作者：洪文明 China Fudan Univereity Institute of Mathematics Shanghai 200433

By investigating the related nonlinear equation, the ergodic theorem is obtained for the super-Browni-an with super-Brownian immigration in two dimension.

关键词： super-Brownian motion immigration ergodic theorem evolution equation.

Semi-uniform Sub-additive ergodic theorems for Skew-product Quasi-flows

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Acta Mathematicae Applicatae Sinica 2014年第2期30卷 359-366页

作者： Jin-ling ZHOU Institute of Applied Mathematics Academy of Mathematics and Systems SciencesChinese Academy of Sciences

The aim of this paper is to extend the semi-uniform ergodic theorem and semi-uniform sub-additive ergodic theorem to skew-product quasi-flows. Furthermore, more strict inequalities about these two theorems are established. By making use of these results, it is feasible to get uniform estimation of the Lyapunov exponent of some special systems even under non-uniform hypotheses

关键词： semi-uniform sub-additive ergodic theorem skew-product quasi-flows

A Generalization of a theorem of Liao

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Acta Mathematica Sinica,English Series 2006年第1期22卷 207-210页

作者： Xiong Ping DAI Zuo Ling ZHOU Depatment of Mathematics Nanjing University Nanjing 210093 P. R. China Lingnan College of Zhongshan University Guangzhou 510275 P. R. China

Let X be a metrizable space and let φ：R× X → X be a continuous flow on X. For any given {φt}-invariant Borel probability measure, this paper presents a {φt}-invariant Borel subset of X satisfying the requirements of the classical ergodic theorem for the contiImous flow （X, {φt}）. The set is more restrictive than the ones in the literature, but it might be more useful and convenient, particularly for non-uniformly hyperbolic systems and skew-product flows.

关键词： ergodic theorem Liao theory

ON THE RANGE OF RANDOM WALKS IN RANDOM ENVIRONMENT　

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Chinese Annals of Mathematics,Series B 1995年第1期16卷 131-138页

作者： ZHOU XIANYIN(Department of Mathematics, Beijing Normal University, Beijing 100875, China.) 北京师范大学北京 100875

The range of random walk on Z￣d in symmetric random environment is investigated. As results, it is proved that the strong law of large numbers for the range of random walk on Zdin some random environments holds if d... 详细信息

关键词： Law of large numbers ergodic theorem Range of random walk Random environment Effective resistance.