非线性算子半群的遍历收敛定理

在Banach空间中引入一般渐近非扩张型半群的广义殆轨道的概念，证明了渐近非扩张型半群的遍历收敛定理等价于相应的广义殆轨道的遍历收敛定理。     

混沌少体系统不可逆过程中的Jarzynski等式

数值研究了混沌少体系统不可逆过程中的Jarzynski等式，并且比较了功和自由能之间的不等式关系，发现Jarzynski等式不止在传统的统计力学适用范围——多体系统远平衡时成立，在混沌少体系统远平衡时也适用。     

Continuous time markov decision processes with interventions

We study Markov jump decision processes with both continuously and instantaneouslyacting decisions and with deterministic drift between jumps. Such decision processes were recentlyintroduced and studied from discrete time approximations point of view by Van der Duyn Schouten.Weobtain necessary and sufficient optimality conditions for these decision processes in terms of equations and inequalities of quasi-variational type. By means of the latter we find simple necessaryand sufficient conditions for the existence of stationary optimal policies in such processes with finite state and action spaces, both in the discounted and average per unit time reward cases.     

Functional ergodic limits for occupation time processes of site-dependent branching Brownian motions in R

We consider a kind of site-dependent branching Brownian motions whose branching laws depend on the site-branching factorσ(·).We focus on the functional ergodic limits for the occupation time processes of the models in R.It is proved that the limiting process has the form ofλξ(·),where A is the Lebesgue measure on IE andξ(·)is a real-valued process which is non-degenerate if and only ifσis integrable.Whenξ(·)is non-degenerate,it is strictly positive for t0.Moreover,ξconverges to O in finite-dimensional distributions if the integral ofσtends to infinity.     

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In this paper, we mainly studied the limit properties for the countable nonhomogeneous Markov chains. We established some limit properties for the functions of the countable nonhomogeneous Markov chains with variables under the convergence in the sense, which extended the similar conclusions for the functions with two variables. At last, as a corollary, we given the similar result in the homogeneous Markov stock market.     

一类随机环境中的随机游动

研究了在环境平稳遍历时,右半直线上可逗留的随机环境中的随机游动的常返性和非常返性,给出非常返、正常返、零常返的充要条件,并讨论了极限性质.作为推论,给出P独立同分布时的相应结论.     

指数稳定双系统同时近似可观测的充分条件

利用指数稳定半群生成元的谱理论,得到了判断指数稳定双系统在[0,∞)同时近似可观测的充分条件.{z1(t)=A1z1(t),z1(0)=x1,y1(t)=C1z1(t)2(t)=A2z2(t),z2(0)=x2,y2(t)=C2z2(t)     

连续遍历系统

我们在这篇文章中,通过扩大遍历系统的条件定义了连续遍历系统,并研究了这种系统和伪轨跟踪性质,强链式传递性质以及影响域之间的关系。进一步我们也给出判别一个常微系统是连续遍历系统的充分条件。     

Integrated Density of States for Ergodic Random Schrödinger Operators on Manifolds

We consider the Riemannian universal covering of a compact manifold M = X/ and assume that is amenable. We show the existence of a (nonrandom) integrated density of states for an ergodic random family of Schrödinger operators on X.