Functional Logarithmic Law Of Two-parameter Brown Motion And Its Increment

The research on Brownian motion and Brownian sheet limit theorem has yielded many profound results.The focus of this paper is also to conduct in-depth research on the related properties of Brownian motion and Brownian sheet.Based on the profound theoretical research results of predecessors,the large deviation method is used as the The main proof tool is to study the two-parameter Brownian motion.The main research contents of this paper are as follows.Chapter 1: As an introduction,it mainly introduces the research background and significance of Brownian motion,some research status at home and abroad,and also expounds some common basic concepts and related properties of Brownian motion and Brownian sheet.Chapter 2: Using the large deviation as a tool,the correlative results of Brown’s single increment are proved and studied,the results of Strassen’s logarithmic law are generalized,and the situation under the consistent norm is extended to the stiuation under the H?lder norm.Chapter 3: The small-time parameter functional logarithm law of Brown singles is studied,and a relatively accurate small-time functional logarithmic law is obtained.Chapter 4: Study of Strassen’s logarithmic law of Brownian motion increments under weighted uniform norm.Chapter 5: In this chapter,the main research done in this paper is summarized first,and then some ideas for the future research directions of the related results are put forward.