Weak and Strong Solutions of Generalized Ito's Stochastic Functional Differential Equations

The fundamental theory of Generalized Itô'a Stochastic Functional Differential Equations (GISFDE), namely, stochastic functional differential equations associated with a stochastic integral based on C-semimartingales, is discussed. The main purpose is to estab- lish the concepts of GISFDE, weak solution, strong solution, solution-measure and several kinds of the uniqueness of solution, to show the relationships among these solutions and get existence and uniqueness theorems of the solution.