Functional Law Of The Iterated Logarithm Of Increments For Brownian Motion And Brownian Sheet

As the core content of probability theory,Brownian motion and Brownian sheet have been studied by many scholars.So far,the study of Brownian motion and Brownian sheet is in the ascendant.The full text mainly discusses the the functional law of the iterated logarithm for Brownian motion and Brownian sheet.We use the large deviations of Brownian motion and Brownian sheet as tools,the existing results are further discussed,generalized and improved.The main research content of this paper are as follows:Firstly,based on the double logarithm law of Brownian motion,we use the large deviation of Brownian motion and the Borel-Cantelli lemma as tools to study the functional triple logarithm law of Brownian motion in depth;then we will explore the Csorgo-Revesz type increment of Brownian motion,and the triple logarithm law of the Brownian motion Csorgo-Révész type increment was derived.Secondly,we discuss the Strassen's law of iterated logarithm for Brownian sheet in detail.In this part,based on the existing research results,with the help of the large deviation in Brownian sheet,the Strassen's law of iterated logarithm is correspondingly proved.Subsequently,the research results are promoted to the Csorgo-Révész type increment of Brownian sheet.Compared with the common derivation method of the law of iterated logarithm in Brownian motion,the method of proof of the law of iterated logarithm is improved.Finally,it mainly explored the iterated logarithm law of Brownian sheet increments under functional.This is different from the research conditions of Strassen's law of iterated logarithm of the increment of Brownian sheet in the previous part,and another type of functional law of iterated logarithm of the increment of Brownian sheet is obtained.There are still many problems worthy of study about the law of the iterated logarithm of Brownian motion and Brownian sheet.At the end of thesis,the next step is given.