Strong Solutions To Stochastic Differential Equations Disturbed By Lévy Processes With Rough Coefficients

In this dissertation,we mainly study the Stochastic Differential Equations(SDEs)disturbed by Lévy process with rough coefficients in d-dimensional(d?1)Euclidean space.We assume that there exists a set SDEs satisfing the strong solutions of the equations and their corresponding Fokker-Planck equations exist.And the equations can approximate to the equation in a certain sense.Thus,we can use the solutions of the Fokker-Planck equations to define some weighted Sobolev spaces in which the coefficients of the equation belong.By using the properties of the Sobolev space in which the coefficients of the equation belong,we obtain the existence and uniqueness of the strong solutions of the equation through quantitative estimates.The most important part of this method is to define the weighted Sobolev space by using the distributions of the solutions of the approximation equations,which makes the equation system studied in this paper more general.In addition,the discussion on the existence and uniqueness of strong solutions to the equation is two independent parts.