Some Theorems For Dependent Sequence Of Irregularity

This paper is divided into two parts, in the first part, we study some strong limittheorems (including the strong limit theorem expressed by inequalities)for several specialdependent discrete random variables; in the second part,we employ adaptive geneticalgorithm to train semi-supervised support vector machines (S3VMs) model for nonlinearpattern recognition. The paper consists of seven chapters.In chapter one, we present the background and the recent development of limittheory of probability theory. Secondly, we briefly introduce the basic ideas and methodsof small deviation theorems of random variable proposed by Liuwen. Thirdly,the currentresearch progress of strong limit theorems for dependent sequence of irregularity and thebackground of semi-supervised learning method based on self-adaptive genetic algorithmare intrduced.Finally,the research ideas and methods of this paper are given.In chapter two, we begin with a special kind of dependent random sequence of PArandom sequence, using the classical limit analysis method and Borel-Cantelli lemma,and thus get a generalization of Kolmogorov irregularity theorems, furthermore we obtainPA sequence of random irregularity theorems.In chapter three, The likelihood ratio and relative entropy as the random measureare used for depicting the dependence random sequence with respect to independencecase,By means of B-C lemma and pure analysis method, some strong limit theorems inform of inequality for arbitrary discrete exponential distribution sequence of irregularityare obtained.In chapter four, let {ξ_n, n≥1} be a sequence of arbitrarily dependent randomvariables under the measure P, and be i.i.d. under the reference measure Q.The likelihoodratio and relative entropy as the random measure are used for depicting the dependence random sequence with respect to independence case,By means of B-C lemma andpure analysis method, some strong limit theorems in form of inequality for arbitrarydiscrete distribution sequence of generalized irregularity are obtained.In Chapter five, The concept of generalized irregularity is applied to Countable Non-homogeneous Markov chains, by means of pure analysis method,a strong limit theoremwhich is about the relative frequency of ordered couple of states is obtained.In Chapter six, The present paper employs adaptive genetic algorithm to train semi-supervised support vector machines (S3VMs) model for nonlinear pattern recognition.Computer simulation results show that this method is much more accurate than tradi-tional gradient method, and the combination of genetic algorithm and gradient methodleads to better accuracy than genetic algorithm.In Chapter seven, Conclusions and some problems we further study.