Stochastic Calculus For Weighted Fractional Brownian Motion And Its Related Processes

This dissertation mainly studies the properties related to derivative for the in-tersection local time(DILT)of weighted fractional Brownian motion(wfBm))and the parameter estimation for non-ergodic Ornstein-Uhlenbeck(O-U)process driven by the wfBm.The full text is divided into three chapters.The first chapter mainly introduces the definition and related properties of wfBm,DILT,non-ergodic O-U process.We also introduce the background of the problems and the present research status.The second chapter studies the DILT of wfBm.We prove the existence and the joint Holder continuity of the DILT.We also study the so-called hybrid quadratic covariation.The third chapter studies the parameter estimation of non-ergodic O-U process driven by wfBm.We prove the strong consistency and the rate consistency of parame-ters.