Limit Properties Of B-Valued Random Walk In Random Environment

Probability theory is a theoretical science of studying regularity of random phenomena, which has been extensively applied in our daily life. Meanwhile, Probability theory is one of the relatively characteristic branches and also an rich and profound topics in modern mathematics.Among them, the random walk in random environments is a historical, active and brand-new topic in probability theory. Moreover, random environment models are widely used in natural science and the social and economic life. In this pa-per,we will focus on discussing convergence properties for B-valued Kesten-Spitzer random walk in random environment on the basis of the the previous theory.This paper is divided into four chapters.In chapter one, we introduce the back-ground and the latest research on random walk in random environment, including some preliminary knowledge and useful lemmas. The second chapter, the third chapter, the fourth chapter is the core of this article. The second discusses the real form for the united form of the strong invariance and the complete convergence of Kesten-Spitzer random walk in random environment. In the p-smooth Banach space, the third involves the complete convergence of Kesten-Spitzer random walk in random environment. The forth introduces the strong law of large numbers for Kesten-Spitzer random walk in random environment in p-smooth Banach space.It generalizes some properties of complete convergence of random walk in random environment.