Extension About The Estimate Inequality Of The Tail Probability Of A Wiener Process

The estimate inequality of the tail probability is very useful in the discussion of the character of a Wiener Process.For example, constant modulus of levy and the increments of a Wiener Process all depend on this inequality. This paper is about the extension of this inequality. And deeply extend it to the case of two-parameter Wiener process.Hope to discuss the increment deeply.It contains three chapters:The first chapter is the introduction .It briefly introduces the Wiener Process as a most important class in the random process. Then it also refers the intimate association with other subjects and the important achievements which have been got in this field of random process. Some prepared workings are also included in this chapter.The second chapter is the prepared knowledge for this paper. In this chapter, we firstly mention the marks used in the paper and the definition of the linear weighted Wiener Process on [t,s]. Secondly we will show some important lemmas and theorems which are used in the proofs of the conclusions in the paper.The third chapter is the proof of the theorem. Firstly, we discuss the estimate inequality of tail probability of a linear weighted Wiener Process which has been defined in the second chapter,Which has the similar conclusion with theorem 1.1.1 in Bibliography. But the conclusion of this paper contains the theorem 1.1.1 in Bibliography 3 bwhich can be considered as the extension of Bibliography 3 on the condition d =1 .Secondly,this paper also discuss the case of two-parameter Wiener process.The two conclusions contained in this paper are extension and creation of the important theorem 1.1.1 and 1.11.1 in Bibliography.In a word, the estimate inequality of tail probability in Wiener process is the basis of the research on the character of Wiener process.Hence the two conclusions...