Stochastic Analysis Of Fractional Brownian Sheet And Its Related Processes

This dissertation aims to study some questions for stochastic analysis of frac-tional Brownian sheet and its related processes. It consists of three chapters.In chapter 1, we introduced some preliminary concepts and necessary prop-erties about fractional Brownian motion, fractional Brownian sheet and stochastic calculus for Gaussian process. We also introduced the background of the problems and the progress of the research.In chapter 2, we considered the approximation of fractional Brownian sheet.We obtained that there exists an unique two parameter wiener integral closest to the fractional Brownian sheet. At the same time, we also studied the properties of the principal functional f, and obtained the existence and uniqueness of the minimizing function of the principal functional f.In chapter 3, we studied the least squares estimator for bridges driven by Gaussian process. By the least squares method, we proved the strong consistency and the asymptotic distributions of the estimator, and then obtained the rate of this convergence.