The Study On The Properties Of Solutions For Several Classes Of Stochastic Differential Equations

The stochastic differential equations have attracted wide attention from scholars in various fields such as biology,engineering,finance and so on.The scholars have done a lot of research work in the field of stochastic differential equations,and have obtained great research results.But there are still many problems that are not deeply studied and deserve further exploration and consideration.So this paper makes corresponding improvement and popularization on the basis of the predecessor.The dissertation is devoted to the important properties of several classes of stochastic differential equations with L(?)vy jumps,which provides some basis for the later study of the solution properties of these types of stochastic differential equations.1.We consider the existence and uniqueness of the solutions for neutral stochastic functional dif-ferential equations with L(?)vy jumps and Markovian switching,and also,we prove the stabilities of the solutions.chave a unique global solution under local Lipschitz condition and more general Khasminskii-type condition,and we also show the stability of the solutions.the neutral stochastic functional differen-tial equations with L(?)vy jumps and Markovian switching global solution is unique when replacing linear growth conditions by Cp inequality,Holder inequality and BDG inequality.These results generalize the corresponding results for stochastic functional differential equations without jumps or Markovian switch-ing.On the basis of Chapter 2,we can obtained the existence uniqueness and stability of global solution of neutral stochastic delay differential equation by when strengthen some conditions,we can also get the existence and uniqueness of the solutions by Cp inequality,Holder inequality and BDG inequality,and we also prove the stability of the solutions.These results generalize the corresponding results for stochastic delay differential equations without jumps or Markovian switching.2.we also consider the Euler-Maruyama method for Neutral stochastic functional differential e-quations with L(?)vy jumps.Under locally Lipschtiz condition and linear growth condition,we prove the numerical solution converges to the real solution by Gronwall inequality,Holder inequality and BDG in-equality.These results generalize the corresponding results for Neutral stochastic functional differential equations with Possion jumps.3.we finally consider exponential stability for neutral stochastic delay differential equations with L(?)vy jumps and Markovian switching.Under locally Lipschitz condition,linear growth and constractive mapping condition,we prove the numerical solution is exponential stability by split-step ? method.These results generalize the corresponding results for neutral stochastic delay differential eqations with Possion jumps and without Markovian switching.