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invariant measures for a Random Evolution Equation with Small Perturbations

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Acta Mathematica Sinica,English Series 2001年第4期17卷 631-642页

作者： Fu Bao XI Department of Applied Mathematics, Beijing Institute of Technology, Beijing 100081, P. R. China Department of Applied Mathematics Beijing Institute of Technology Beijing 100081 P. R. China

In this paper we consider a random evolution equation with small perturbations, and show how to construct coupled solutions to the equation. As applications, we prove the Feller continuity of the solutions and the existence and uniqueness of invariant measures. Furthermore, we establish a large deviations principle for the family of invariant measures as the perturbations tend to zero.

关键词： invariant measures Large deviations Coupling Random evolution equation

Decay Parameter and invariant measures for Markovian Bulk-Arrival Queues with Control at Idle Time

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Decay Parameter and Invariant Measures for Markovian Bulk-Ar...

Decay parameter and related properties of n-type branching processes

第八届中国不确定系统年会

作者： Li Junping Chen Anyue Central South University,China, Liverpool University,UK,

＜正＞We consider properties regarding decay parameter and the associated invariant measures for Markovian bulk-arrival Queues with control at idle *** exact value of the decay parameter for such model is *** corresponding subinvariant and invariant measures are considered and the structure of all the subinvariant and invariant measures are presented.

关键词： Decay parameter invariant measures Quasi-stationary distribution Queueing model

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Science China Mathematics 2012年第12期55卷 2535-2556页

作者： LI JunPing WANG Juan School of Mathematics and Statistics Central South University Changsha 410075 China

We consider decay properties including the decay parameter, invariant measures, invariant vectors, and quasistationary distributions for n-type Markov branching processes on the basis of the 1-type Markov branching processes and 2-type Markov branching processes. Investigating such behavior is crucial in realizing life period of branching models. In this paper, some important properties of the generating functions for n-type Markov branching q-matrix are firstly investigated in detail. The exact value of the decay parameter λC of such model is given for the communicating class C = Zn+ \ 0. It is shown that this λC can be directly obtained from the generating functions of the corresponding q-matrix. Moreover, the λC -invariant measures/vectors and quasi-distributions of such processes are deeply considered. λC -invariant measures and quasi-stationary distributions for the process on C are presented.

关键词： n-type Markov branching process decay parameter invariant measures invariant vectors quasi-stationary distributions

Recurrence of Transitive Points in Dynamical Systems with the Specification Property

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Acta Mathematica Sinica,English Series 2018年第12期34卷 1879-1891页

作者： Xiao Yi WANG Yu HUANG School of Mathematics and Statistics Zhaoqing University Zhaoqing 526061 P. R. China Department of Mathematics Sun Yat-sen University Guangzhou 510275 P. R. China

Let T ： X →X be a continuous map of a compact metric space X. A point x E X is called Banach recurrent point if for all neighborhood V of x, （n ∈ N ： T^n（x） ∈ V} has positive upper Banach density. Denote by Tr（T）, W（T）, QW（T） and BR（T） the sets of transitive points, weakly almost periodic points, quasi-weakly almost periodic points and Banach recurrent points of （X, T）. If （X, T） has the specification property, then we show that every transitive point is Banach recurrent and O≠ W（T） n Tr（T） ≠ W＊（T） ∩ Tr（T） ≠ QW（T） ∩ Tr（T） ≠ BR（T） ∩ Tr（T）, in which W＊（T） is a recurrent points set related to an open question posed by Zhou and Feng. Specifically the set Tr（T） M W＊（T）／ W（T） is residual in X. Moreover, we construct a point x E BR ／ QW in symbol dynamical system, and demonstrate that the sets W（T）, QW（T） and BR（T） of a dynamical system are all Borel sets.

关键词： Specification property invariant measures recurrent points measure center

Decay parameter and related properties of 2-type branching processes

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Science China Mathematics 2009年第5期52卷 875-894页

作者： LI JunPing School of Mathematical Science and Computing Technology, Central South University, Changsha 410075, China 1. School of Mathematical Science and Computing Technology Central South University Changsha 410075 China

We consider the decay parameter, invariant measures/vectors and quasi-stationary dis- tributions for 2-type Markov branching processes. Investigating such properties is crucial in realizing life period of branching models. In this paper, some important properties of the generating functions for 2-type Markov branching q-matrix are firstly investigated in detail. The exact value of the decay parameter λC of such model is given for the communicating class C = Z+2 \ 0. It is shown that this λC can be directly obtained from the generating functions of the corresponding q-matrix. Moreover, the λC-invariant measures/vectors and quasi-distributions of such processes are deeply considered. A λC-invariant vector for the q-matrix (or for the process) on C is given and the generating functions of λC-invariant measures and quasi-stationary distributions for the process on C are presented.

关键词： 2-type Markov branching process decay parameter invariant measures invariant vectors quasi-stationary distributions 60J27 60J80

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Progress in Natural Science:Materials International 1998年第1期 25-35页

作者：任福尧周吉邱维元 China Department of Mathematics Fudan University Shanghai 200433

The existence and uniqueness of the self-similar measure on the Julia sot of single rational function are discussed A self-similar measure is constructed on the Julia set of the random iteration of rational functions, which shows that under certain conditions the measure is unique and non-atomic; moreover its support is exactly equal to that of the Julia set. Finally some applications of the self-similiar measures to condensed matter physics and statistical physics are given.

关键词： invariant measures Fatou sets Julia sets random dynamical systems.