Extension About How Big Are The Increments Of A Wiener Process

This paper is about the increments of a Wiener Process on the condition of a linear weighted model.It contains three chapters.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.In order to discuss the increments of a Wiener Process deeply,we will use the extension of this inequality (Bibliography 1) and constant modulus of levy(Bibliography3).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 how large the increments of a linear weighted Wiener Process which has been defined in the second chapter. We also prove the similar conclusion with Bibliography 21 on the condition that we give a new regularizing factor β_T But the conclusion of this paper contains Bibliography 3 which can be considered as the extension of Bibliography 3 on the condition d = 1, in the regularizing factor β_T and the weighted linear combination S_t,sIn a word, the qualities of the increments in a Wiener Process are the basis of the research on the law of iterated logarithm in a Wiener Process. We can also think about a two-parameter Wiener process and how small are the increments of a Wiener...