Sample Properties Of Generalized Levy Sheet

Levy sheet is a special independent increment process of zero initial valueand two-parameter,it combine with the Brown sheet of continuous type and thePoisson sheet of discrete type to study,however, generalized Levy sheet is moregeneral,and has a very wide range of applications in economic and financial, etcmany fields, but few scholars carry on the comprehensive and systematic research.In this paper,We define the Levy sheet and generalized Levy sheet,then ex-tend some of the sample properties of Levy sheet to generalized Levy sheet,suchas random continuity and separability,and some of its local property,here, we get alot of important results. In the end, we discuss the tangent function of generalizedLevy sheet.This paper is divided into four chapters, the first chapter presents the re-search background, summarizes the main work of this paper, and give some pre-requisites that the study will use. The second chapter we simply give the sampleorbital properties of Levy sheet, the third chapter,we extend some of the sampleproperties of Levy sheet to generalized Levy sheet and discuss the tangent func-tion of generalized Levy sheet, the second chapter and the third chapter is thefocus of this paper. The fourth chapter presents some application fields of thegeneralized Levy sheet and several problems of this paper existing in the courseof the study.