Some Results Of Weighted Linear Wiener Process

This paper is the discussion on how large the increments and the modulus of non-differentiability of a Wiener Process on the condition of a linear weighted model. 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 weightedWiener Process on [t,s]. Secondly we mention some important lemmas andtheorems 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 Theorem 1.2.1 inBibliography 3 on the condition that we give a new regularizing factor β_T . But theconclusion of this paper contains Theorem 1.2.1 in Bibliography 3 which can be considered as the extension of Theorem 1.2.1 in Bibliography 3 on the condition d -1 in the regularizing factor β_T and the weighted linear combination S_(t,s).Secondly, we give the proof of the theorem about the modulus of non-differentiability in linear weighted Wiener Process, which is the extension of Theorem 1.6.1 in Bibliography 3 about the modulus of non-differentiability in Wiener Process. As the same to the first conclusion, we just consider it as Theorem 1.6.1 in Bibliography 3 about the modulus of non-differentiability in Wiener...