Tempered Fractional ?-stable L(?)vy Motion

Nowadays,Anomalous diffusion behavior is widely used in many fields.With the development of stochastic differential problems,we have begun to study the fractional Brownian motion and the fractional ?-stable Levy motion,In this paper,the tempered fractional ?-stable Levy motion is discussed on the basis of the stochastic process dis-cussed earlier.This article is mainly divided into five chapters.The first chapter mainly in-troduces the development and some important results of the tempered fractional Brownian motion and the fractional ?-stable Levy motion.The second chapter follows the related important conclusions of the first chapter and discusses the definition,integral structure,self-similarity and stationary increment of the tempered fractional ?-stable Levy motion.The conclusion is proved by numerical simulation.Then we will consider the Fokker-Planck equation of this motion.In the third chapter,by defining the increment process of tempered fractional ?-stable Levy motion,introducing the Codifference and Covari-ation statistics,using a series of calculations,the long-range dependence of increments is discussed,and the influence of the parameter ? on the long-range dependence is com-pared.The fourth chapter discusses the path properties of the tempered fractional ?-stable Levy motion,including continuity,measurable version,separable version,integrability,and so on.At the same time,the fast Fourier transform method is used to simulate the particle trajectory and compare the influence of parameters on the path.Then the wavelet coefficient is introduced to construct a new stochastic process.What is more,this new stochastic process is also a stable process.And its time scale also has self-similarity.In the last chapter,we will compare tempered fractional Brownian motion with tempered fractional ?-stable Levy motion.