Stochastic Calculus For Two Extension Process Of Fractional Brownian Motion

This dissertation aims to study some questions for two kinds of self-similar process related to fractional Brownian motion. It consists of three chapters.In chapter 1, we introduce some preliminary concepts and necessary properties about fractional Brownian motion, subfractional Brownian motion and Rosenblat-t process. We also introduce the background of the problems and the present research status.In chapter 2, we consider the intersection local time of Ornstein-Uhlenbeck driven by subfractional Brownian motion (subfractional O-U process in short).We prove the subfractional O-U process is local nondeterministic, and establish some estimates about the increment of this process. We give the necessary and sufficient condition for the intersection local time of subfractional O-U process by using the local nondeterminism.In chapter 3, we study the weak limit theorem of the Rosenblatt sheet.We prove the convergence in law of two families of process to the Rosenblatt sheet: the first one is constructed from a Poisson process in the plane and the second one is based on random walks.