The Limit Theorem Of Multi-type Branching Process In Random Environment

The study of limit theorems of the multi-type branching process in random environment has aroused the interest of many scholars in recent years.In some published articles,some scholars have explored some limit theorems for the multi-type branching process in random environment.The research results are applied to random walks.On the basis of previous academic research,this thesis will further study limit theorems of multi-type branching process in random environment.The article is divided into four chapters.The first chapter is introduction.We introduce the background and development status of the multi-type branching process in random environment,give the definition of multi-type branching process in random environment,and give some limit theoretical results of multi-type branching process in random environment.We summarize the main results of these papers.In the second chapter,we prove the convergence of LP about the multi-type branching process in random environment.The sufficient conditions for the convergence of the normalization process according to LP are found.The convergence of L1 is obtained by probability convergence and uniform convergence.In the third chapter,we carry out further research on the basis of previous studies and obtain the central limit theorem of the multi-type branching process in random environment.