The Existence And Uniqueness Of The Solution For Stochastic Functional Differential Equations With Infinite Delay And Markovian Switching

Stochastic differential equations with markovian switching have played more promi-nent role in people's daily lives,its equation theory get more and more people's attention,but when it come to stochastic functional differential equations with infinite delay andmarkovian switching(ISFDEwMS),few study have been found.This article solve the ex-istence and uniqueness of the solution which is the most essential in qualitative theoryfor such equations.This paper mainly discusses the existence-and-uniqueness theorem ofsolution for ISFDEwMS in boundary continuous function space BC((-∞,0]; R~n) andspace Ch.It is divided into five chapters.Chapter1 offers the research back ground of this paper and introduces the problemthe author will solve.In Chapter2,some notations,necessary definitions and useful lemmas which will playa great role in the next proof are introduced.The existence-and-uniqueness theorem of ISFDEwMS is established in phase spaceBC((?∞,0];Rn) in Chapter 3.Under the uniform Lipschitz condition,we weaken thelinear growth condition to obtain the existence-and-uniqueness theorem of solution forISFDEwMS. Further, under the linear growth condition,the uniform Lipschitz conditionis replaced by the local Lipschitz condition, we find that existence-and-uniqueness theo-rem is valid for ISFDEwMS on finite interval.Finally existence-and-uniqueness theoremholds on the entire interval for ISFDEwMS.Chapter 4 deals with the existence-and-uniqueness of stochastic functional differ-ential equations in Phase space Ch.We make use of weakening the linear growth con-dition and the uniform Lipschitz condition, to obtain the existence-and-uniqueness the-orem for stochastic functional differential equations. Additionally, we assume that thelinear growth condition and the local Lipschitz condition hold,then the existence-and-uniqueness theorem is also derived on finite interval for ISFDEwMS.In addition,theexistence-and-uniqueness theorem holds for ISFDEwMS on the entire interval.At the end of this paper the author summarizes the innovations and shows the con-clusions of this paper.Finally,related literatures are listed.