The Rate Of Convergence In The Functional Limit For Increment Of A Brownian Motion For Small Time Parameter

Many representative results have been obtained in the study of functional limit theorems of Brownian motion increment.In this dissertation,based on some important study results of predecessors,and through my thorough exploration,through the improvement of the previous study conditions,with the large small deviations of Brownian motion orbit as the proof tool,the convergence rate of Brownian motion increment in several cases of small time parameters of the functional limit.The major study details of this dissertation are as follows:Chapter 1: The study backdrop and meaning of the Brownian motion of the subject is briefly explained.At the same time,the development process of the Brownian motion of the subject and some domestic and overseas study status are also introduced.Finally,the key definition and nature of the Brownian motion of the subject are also slightly clarified.Chapter 2: The small time parameter functional limit of Brownian motion increment is discussed,and the small time Chung logarithm law is obtained using large and small deviations as tools.Chapter 3: Brownian motion increment is discussed in the case of H(?)lder norm,and using large and small deviations as tools,the small time Chung logarithm law under H(?)lder norm is obtained.Chapter 4: Brownian motion increment is discussed in the capacitive sense,and the small time Chung logarithm law in the(r,p)-capacitive sense is obtained by using capacitive instead of probability using large and small deviations as tools.Chapter 5: This chapter first summarizes the study done in this dissertation,and then predicts some relevant results in future study directions.