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REPRESENTATION OF ADDITIVE FUNCTIONALS AND LOCAL TIMES FOR jump MARKOV processES AND THEIR FUNCTIONAL LIMIT THEOREM

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Acta Mathematica Scientia 2003年第1期23卷 117-123页

作者：蒋义文刘禄勤 DepartmentofMathamatics WuhanUniversityWuhan430072ChinaMilitaryEconomicAcaldemyWuahn430035China DepartmentofMathematics WuhanUniversityWuhan430072China

The representation of additive functionals and local times for jump Markov processes are obtained. The results of uniformly functional moderate deviation and their applications to birth-death processes are also presen... 详细信息

关键词： Additive functional q-process local time moderate devaition jump process

Existence and Application of Optimal Markovian Coupling with Respect to Non-Negative Lower Semi-Continuous Functions

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Acta Mathematica Sinica,English Series 2000年第2期16卷 261-270页

作者： Shaoyi ZhangDepartment of Mathematics.Beijing Normal University,Beijing 100875,P.R.China Department of Mathematics,Hubei Normal University,Huangshi 435002,P.R.China Department of Mathematics Beijing Normal University Beijing 100875 P. R. China Department of Mathematics Hubei Normal University Huangshi 435002 P. R. China

In this paper,for two given transition probabilities,the existence of the optimal Markovian coupling with respect to a non-negative lower semi-continuous function is *** an application of this result,the well-known Strassen’s theorem is ***,it is proved that the existence of an order-preserving Markovian coupling of two given jump processes is equivalent to their stochastical comparability.

关键词： Transition probability Markovian coupling jump process

Exponential stability of stochastic generalized porous media equations with jump

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Applied Mathematics and Mechanics(English Edition) 2014年第8期35卷 1067-1078页

作者：郭柏灵周国立 Institute of Applied Physics and Computational Mathematics College of Mathematics and Statistics Chongqing University

Stochastic generalized porous media equation with jump is considered. The aim is to show the moment exponential stability and the almost certain exponential stability of the stochastic equation.

关键词： stochastic generalized porous media equation jump process stability

Nash Inequalities for General Symmetric Forms

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Acta Mathematica Sinica,English Series 1999年第3期15卷 353-370页

作者： Mufa Chen Department of Mathematics, Beijing Normal University, Beijing 100875, P. R. China Department of Mathematics Beijing Normal University Beijing P. R. China

This paper deals with the Nash inequalities and the related ones for general symmetric forms which can be very much unbounded. Some sufficient conditions in terms of the isoperimetric inequalities and some necessary conditions for the inequalities are presented. The resulting conditions can be sharp qualitatively as illustrated by some examples. It turns out that for a probability measure, the Nash inequalities are much stronger than the Poincare and the logarithmic Sobolev inequalities in the present context.

关键词： Nash inequality Symmetric form Isoperimetric Inequality jump process

THE EQUILIBRIUM PROBLEM AND CAPACITY FOR jump MARKOV processES

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Acta Mathematica Scientia 1995年第1期15卷 15-30页

作者：刘禄勤 Dept of Math. Wuhan University Wuhan 430072 China

Let X=(Omega,F,F-t,X(t),theta(t),P-x) be a jump Markov process with q-pair q(x)-q(x, A). In this paper, the equilibrium principle is established and equilibrium functions, energy, capacity and related problems is inve... 详细信息

关键词： MARKOV process jump process EQUILIBRIUM PRINCIPLE ENERGY CAPACITY EQUILIBRIUM FUNCTION

Optimal Markovian Couplings

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Progress in Natural Science:Materials International 1994年第3期 111-113页

作者：陈木法 Beijing 100875 Beijing Normal University Department of Mathematics PRC

In the past twenty years, the coupling method has grown up step by step, it isnow a fundamental mathematical tool for studying the probability theory and has al-ready found wide applications. Very recently, it has been applied successfully bythe author and F.Y. Wang to the estimation of the first eigenvalue of Laplacian onmanifold. The coupling of two stochastic processes is to construct a bivariate process,called coupling process, so that the original processes become the marginals of the

关键词： Markovian coupling optimal coupling jump process diffusion process.

基于状态空间的贝叶斯跳跃厚尾金融随机波动模型研究

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