条件概率测度

Firstly, we consider the problem of the representation formula for the transition probability density of a right process under Girsanov transform. Secondly,we consider the problem of the MEMMs (minimal entropy martingale measure)for Markov switching Levy processes, and justify that the minimal entropy martingale measure is obtained by some regime switching Esscher transform. At last,we consider the problem of the invariant measure and the ergodic property of recurrent right processes. This paper includes 5 chapters.

首先，我们考虑了满足一定条件的右过程在Girsanov变换下的转移概率密度的表达式问题；其次，我们考虑了由Markov调制的Lévy过程的最小相对熵鞅测度的问题，证明了其最小相对熵鞅测度是某个状态转换Esscher变换；最后，我们考虑了右过程的不变测度及其遍历性的问题。

According to the Logistic Equation and the impact of stochastic factors, a stochastic nonlinear dynamical model had been presenred. The max Lyapunov exponent was calculated by Oseledec multiplicative ergodic theory, the local stability conditions had been obtained; the global stability conditions had also been obtained by judging the modality of the singular boundary; the stochastic Hopf bifurcation was analyzed using the invariant measure of stable probability density, and the condition of stochastic Hopf bifurcation had been discussed. The key parameter impacting the urban domestic water consumption had been found by numerical emulation.

根据Logistic阻滞增长模型原理，考虑到诸多随机因素的影响，本文建立了一个城市生活用水量的随机非线性模型，运用Oseledec乘性遍历定理计算了模型的最大Lyapunov指数，得到了局部稳定性的条件；通过对扩散边界性态的分析，得到了全局稳定性的条件；通过分析系统平稳状态概率密度的不变测度，得到了模型随机Hopf分岔的条件，结合实际进行了数值仿真，得到了影响用水量的关键参数。

Firstly,the classification of probability rule is analyzed on the base of classic rough set concepts and extended to the equal relation of set in the indefinite system,namely,the upper and lower approximation space of research set is expressed in the form of conditional probability;then,according to the measure of probability rule,the attributes reduction is carried out and the classification rule is extracted by using the related parameters of condition attributes' impend precision from the angle of conditional probability;Finally,the related simulation test result is given and the result shows the classification rules with probability measures is more rational.

首先在经典粗糙集概念的基础上分析概率规则的分类，并将其推广到不确定系统的集合等价关系中，即用条件概率的形式表示研究集合的上下近似空间；然后根据概率规则的测度从条件概率的角度利用条件属性的逼近精度的相关参数进行属性集的约简进而提取分类规则；最后给出了相关的仿真实验结果，结果表明带有概率测度的分类规则更合理。

Limit theorems for the integration of function sequence with respect to weak convergence probability measure sequence are proved under the condition of the weak tight, which have been used to research the some convergence of expectant functional sequence,and a sufficient condition for the epi-convergence of expectant functional sequence is obtained.

提出了弱胎紧的概念，并在弱胎紧的条件下证明了函数序列关于弱收敛概率测度序列积分的极限定理，用其研究了期望泛函序列的若干收敛性，得到了期望泛函序列的、上图收敛的一个充分条件。

The asymptotic unbias edness and the strong consistency and rate of convergence under given conditions are obtained.

在测度弱收敛的意义下，研究了一般概率测度μ的核估计μn，得到了它的渐近无偏性、强相合性及在给定条件下的收敛速度。

Singer Leona Lewis and former Led Zeppelin guitarist Jimmy Page emerged as the bus transformed into a grass-covered carnival float, and the pair combined for a rendition of "Whole Lotta Love".

歌手leona刘易斯和前率领的飞艇的吉他手吉米页出现巴士转化为基层所涵盖的嘉年华花车，和一双合并为一移交&整个lotta爱&。

This is Kate, and that's Erin.

这是凯特，那个是爱朗。