The Complete Convergence For Random Walk In Random Scenery

Theory of probability is a science of studying regularity of random phenomena,which is extensively applied in nature science,technological science and social science etc. Probability Limit Theory is one of the branches of science of probability.Convergence is an important conception in Probability Limit Theory. There are a series of convergence conceptions such as convergence in probability,convergence in distribution,almost sure convergence etc. In this paper,we discuss the complete convergence for Kesten-Spitzer random walk in random scenery.This thesis is based on the fruits of others and discuss the complete convergence for random walks in random sceneries. We prove the complete convergence for random walks in random sceneries, some mild sufficient conditions for complete convergence are obtained. To prove this theorem, we use the method of truncation.This paper is divided into three chapters. In chapter one, we introduce the background and the latest research on random walks in random sceneries,including some lemmas and useful inequations. In chapter two and three, we prove five theorems and their deductions.