The Fractal Nature Of Volterra Process

Stochastic process theory, mainly through observe the evolution of the process of random phenomena, to deduce its statistical regularity. Volterra Process is given by M(t)=0 tF(t,r)dX(r), t?R+,It is a sort of stochastic processes.Volterra Process has a close relationship with physical motions, such as White noise,Brownian motion and so on.In the study of the fractal analysis and stochastic process,determining the fractal dimension of stochastic process is a very active subject.In this thesis, the major part is studying the fractal nature of Volterra Process. In the recent literature, Eyal Neuman assume that the integrand is a function of smooth variation and derived the fractal dimension of Volterra Process.In this paper, we redefine the integrand of Volterra Process based on the results of the study,and present a more universalizability fractal nature of Volterra Process: 1.hM(t)?1, (?)t?SlX,P-a.s. 2.dim(Q?M)=??, (?)?? [0,1/?], P-a.s. Where l?0 is some constant which is related to F(t,r),?>0 is some parameter determined by Levy measure ?(dx).