The Occupation Time And Potential Measures Related To The Last Exit Time

In recent years,a series of achievements have been made in the study of occupation time by spectrally negative Levy process,the study of occupation time and potential measure related to the last exit time has attracted extensive attention of scholars.Some scholars use different methods to determine the distribution and Laplace transform for the occupation time.In this paper,we study the specific expressions for occupation time and potential measures of spectrally negative Levy process related to the last exit time.The details are as followsIn chapter 1,we summarize the research status of space occupation time and potential measure of spectral negative Levy process at home and abroad,introduce the different methods for studying the Laplace transform of occupation time,and finally gives the main research results of this paper.In chapter 2,we review the properties of spectral negative Levy processes and the related scale functions,fluctuation identities,The basic theories of Poisson method and perturbation method used in this paper are described.In chapter 3,we adopt poisson method and perturbation method to study the joint Laplace transform of the last exit time,occupation time and process value for spectrally negative Levy process,and verify the results obtained.In chapter 4,we research the specific expression of the potential measure related to the the last exit time of spectral negative Lévy processes,In chapter 5,we adopt poisson method to study the joint Laplace transform of two occupation time for spectrally negative Levy process.and T0+=sup{t≥0:Xt<0},T0-=sup{t≥0:Xt>0},τ-a-=inf{t>0:Xt<-a},τa+=inf{t>0:Xt>a},with the convention sup ?=0,inf ?=∞.