Theory Of The Existence And Boundedness For Stochastic Differential Equations

Existence and boundedness theory for the stochastic differential equations are mainly investigated in this thesis, which improve the existence-uniqueness theorem for the stochastic differential equations and stochastic functional differential equations. A series of new definitions have been established. A number of new criteria on the boundedness for the solutions of stochastic differential equations are obtained by using Lyapunov straight method. The new results will be illustrated by many examples. New definitions and theorem have been established on the increase order estimate for the solutions of stochastic differential equations.The whole thesis is divided into five chapters.Chapter 1. It offers some relative knowledge including basic concepts, theorem and inequality for the stochastic differential equations.Chapter 2. It offers the results of existence-uniqueness theorem for the stochastic differential equations obtained by [15]. Then follows we do further improvement to existence-uniqueness theorem for the stochastic differential equations and stochastic differential functional equations.Chapter 3. It offers new definitions on the boundedness for the solutions of stochastic differential equations as well as new theorem on the boundedness for the solutions of stochastic differential equations.Chapter 4. It offers new definitions and theorem on the estimate increase order for the solutions of stochastic differential equations. Which are illustrated by examples.At the end of the thesis,The innovations, further study direction and many related references are listed.