Some Strong Laws Of Large Numbers For Stochastic Process Indexed By A Tree

In recent years,the tree model that developed has been applied to many fields,such as statistics,physics and finance,etc.The research of the strong law of large numbers has held an important position in the development process of probability theory,and the strong law of large numbers is one of the central issues of the international probability theory.The stochastic process is an important branch of probability theory,so researching in the field has very high theoretical significance and application value.The main content is based on a class of special non-homogeneous tree T in this paper.we construct different t_n(?,?)firstly,and prove the t_n(?,?)is a non-negative martingale under the measure P.Then some conclusions about the strong law of large numbers for tree-indexed stochastic processes are given and proved by applying Doob's martingale convergence theorem,some important inequalities and the properties of superior limit.In the first place,the research of the paper is carried out on the m-ordered non-homogeneous Markov sources indexed by a tree,and a prove for the strong deviation theorem is given.In the next place,we give a strong deviation theorem for the m-ordered Markov chains of generalized gambling systems indexed by a tree.In the end,we give a class of small deviation theorems for the m-ordered non-homogeneous Markov information sources on the tree.At the same time,the relevant inferences are given and proved,which enriches the content of the strong law of large numbers.