半直线上的独立随机环境中的随机游动

本文给出环境独立时半直线上随机游动的模型.在假定环境满足一定的条件下,证明了一个强大数定律,运用该定律讨论了过程常返性及非常返的判定.     

Excessiveness of harmonic functions for certain diffusions

In an earlier paper⁽⁴⁾ the author has shown that a diffusion process whose potential kernel satisfies certain analytic conditions has all of its excessive harmonic functions, which are not identically infinite, continuous. This paper shows that under these conditions (concerning its potential kernel), the excessiveness of its nonnegative harmonic functions isautomatic.     

Recurrence and transience properties of some neural networks: an approach via fluid limit models

The subject of the paper is the stability analysis of some neural networks consisting of a finite number of interacting neurons. Following the approach of Dai [5] we use the fluid limit model of the network to derive a sufficient condition for positive Harris-recurrence of the associated Markov process. This improves the main result in Karpelevich et al. [11] and, at the same time, sheds some new light on it. We further derive two different conditions that are sufficient for transience of the state process and illustrate our results by classifying some examples according to positive recurrence or transience. This revised version was published online in June 2006 with corrections to the Cover Date.     

Some Limit Results for Transient Subsequence of Brownian Motion on Line

Ｌｅｔ {Ｗ(ｔ) ,0≤ｔ<∞ }ｂｅａｓｔａｎｄａｒｄ ,ｏｎｅ ｄｉｍｅｎｓｉｏｎａｌＢｒｏｗｎｉａｎｍｏｔｉｏｎｏｎ (Ω ,Ｆ ,Ｐ) .Ｉｔｉｓｗｅｌｌｋｎｏｗｎｔｈａｔ -∞ =ｌｉｍｉｎｆｔ→∞ Ｗ(ｔ) <ｌｉｍｓｕｐｔ→∞ Ｗ(ｔ) =∞ａｎｄａｃｃｏｒｄｉｎｇｔｏＫａｈａｎｃｅ ([1 ] ,Ｔｈｅｏｒｅｍ1 ,Ｃｈａｐｔｅｒ 1 2 ) ,ｉｆａｓｅｑｕｅｎｃｅ {ｔｎ,ｎ≥ 1 )ｓａｔｉｓｆｉｅｓ∑∞ｎ=11ｔｎ<∞ ,ｔｈｅｎｌｉｍｎ→∞ Ｗ(ｔｎ) =∞ａ .ｓ.Ｗｅｃａｌｌｔｈｅｓｅｑｕｅｎｃｅ {Ｗ (ｔｎ) ,ｎ≥ 1 }ａｔｒａｎｓｉｅｎｔ…     

The Weighted Transience and Recurrence of Markov Processes

Transience and recurrence are among the most important concepts in Markov processes. In this paper, we study the transience and recurrence for right processes with a given weight function, and characterize them by potentials, excessive functions, first hitting times and last exit times of the process. We also study the properties of recurrent states.     

Recurrence and invariant measure of Markov chains in double-infinite random environments

The concepts of π -irreduciblity, recurrence and transience are introduced into the research field of Markov chains in random environments. That a π -irreducible chain must be either recurrent or transient is proved, a criterion is shown for recurrent Markov chains in double-infinite random environments, the existence of invariant measure of π -irreducible chains in double-infinite environments is discussed, and then Orey’s open-questions are partially answered.     

随机环境中马氏链的常返性和瞬时性

在π-不可约条件下,得到随机环境中的马氏链瞬时和常返的判定准则,进而得到随机环境中马氏链常返的充要条件;如果环境还是平稳的,则状态空间中不存在非正则本质态.     

随机环境下的MTAR模型的几何遍历性

在本文中,提出了随机环境下的MTAR模型的非常返性及其确定的导出序列几何遍历的几个充分条件.     

On Symmetric Stable-Like Processes: Some Path Properties and Generators

We derive some path properties of symmetric stable-like processes constructed via Dirichlet form theory and then sufficient conditions in order that the generators of the forms contain a nice functions space, are given.     

On the stability of crystal growth

We investigate properties of solid-on-solid models for crystal growth, involving general microscopic rates of capture of atoms by the crystal surface and of escape of atoms. The rates in this Markov process influence the stability of the growing surface. We prove, for various different ranges of the rate parameters, stability (i.e., ergodicity) and instability (i.e., nullity) of the growth process. Symmetry properties of the process, such as reversibility, dynamic reversibility, and reflection invariance, are proved or disproved under various conditions. We give a measure of surface smoothness that distinguishes between stable and unstable growth.