遍历性

Chapter 1 gives the background,current research process of relatedproblems and summarizes this thesis\'s work.In chapter 2,we study the Brownian motion with holding and jumping on the boundary.We use the resolvent method to obtain the infinitesimal generator because the domain of the infinitesimal generator is essentially the same as the range of the resolvent.Knowledge of this range and of the differential operator determines uniquely the infinitesimal generator.Since the semigroup generated by the DHJ is not strongly continuous,to use the nice property of strongly continuous semigroup in analytic theory,in chapter 3 we show that the dual is strongly continuous and derive ergodicity through spectral radius formulas and finally obtain the ergodic theorem by duality. In chapter 4,we discuss a class of a more general process---one dimensional Feller diffusion proposed by W.Feller in 1954.The Feller diffusion allows the possibility of jumps from boundary to boundary,not only from boundary to the interior.We give the stationary distribution of this process.

具体地，本文的结构如下：第一章给出了问题产生的背景，研究现状及本文的主要工作；第二章研究了在边界上逗留后随机跳的布朗运动，我(来源：3dABC论文网www.abclunwen.com)们用预解算子的方法得到其无穷小生成元，因为无穷小生成元的定义域本质上就是预解算子的值域，知道这个值域和微分算子形式就能唯一地决定无穷小生成元；由于DHJ过程产生的半群不是强连续的，为利用强连续半群的一些漂亮性质，在第三章中我们证明其对偶半群是强连续的，然后由谱半径公式得到遍历性并且最后由对偶得到遍历定理；第四章讨论了Feller在1954年引入的更广的一类过程----一维Feller扩散过程，Feller扩散过程允许有从边界到边界的跳发生，即不仅仅局限于从边界到内部的跳，在这一章中，我们给出了一维Feller扩散过程的平稳分布；在第五章，我们讨论了一些相关的问题，给出了DHJ过程对应的PDE问题及特征值与收敛速度的关系。

In chapter 5, we obtain the invariant measure and the ergodic property of recurrent right processes.

在第五章里，我们得到了常返右过程的不变测度的存在性、唯一性及其遍历性。

By use of the ergodic property of chaos movement and the inversion of genetic algorithm, a chaos genetic algorithm was proposed. Its basic principle lies in the small disturbance of which extent is adjusted during searching to child generation group using the chaos variable.

摘 要：利用混沌优化的遍历性和遗传算法优化的反演性，提出了混沌遗传算法，其基本思想是把混沌变量加载于遗传算法的变量群体中，利用混沌变量对子代群体进行微小扰动，随着搜索过程的进行逐渐调整扰动幅度。

For a class of bilevel multi-objective decision,this paper converts it into the problem of equivalent single-level multi-objective decision,then makes use of the inversion property of the genetic algorithm with the ergodic property of the chaos optimization method.

针对求解一类二层多目标决策问题，首先将其转化为等价的单目标决策问题，然后利用遗传算法优化的反演性和混沌优化方法的遍历性，并结合精确不可微罚函数求解非线性约束优化问题，提出了求解此类问题的混沌遗传算法。

The purpose of this article is to give some equivalent conditions for ergodicity and unique ergodicity.

给出遍历性及唯一遍历的几个等价条件。

At the same time the ergodicity of the quotient space is proved using the ergodicity of the original space.

同时利用原空间的遍历性可以证明商空间的遍历性。

From the ergodicity and the regularity of chaotic behavior,it is conclude that the algorithm has the asymptotical convergence property.

基于变分不等式的等价形式，构造了一种混沌搜索算法来直接求解变分不等式问题，根据混沌行为的遍历性和规则性，可以得到算法的渐进收敛性。数值试验结果表明，该算法是一个有效的方法

Let P be a Markov operator in, and Q any ergodic Markov operator possessing finite invariant measure. In this note a simple and direct proof of the equivalence of the mixing property for Q and the ergodicity for Cardesian product PQ is given.

设P是L上的Markov算子，Q是任一具有有限不变测度并且遍历的Markov算子，在这篇注记中我们给出了P的混和性和Cartesian积P×Q的遍历性相互等价这一结果的直接而简单的证明。

Therefore, there exist the problems of slow convergence speed and local optimum.

由于混沌具有其独特性质，如内随机性、遍历性和规律性，特别是混沌的遍历性特点可作为搜索过程中避免陷入局部极小的一种优化机制。

Obtain the necessary and sufficient conditions of ergodic and exponentially ergodic properties for the population process.

给出了人口过程遍历性与指数遍历性的充分必要条件。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新