The Properties Of Euler-Maruyama Numerical Solutions Of Neutral Stochastic Functional Differential Equations

Neutral functional differential equations not only depend on present and past states but also involve derivatives with delays.It has widely been used into many fields,such as chemical reaction process,transmission process,heat exchange process,large-scale integrated circuit,etc..When neutral functional differential equation is subjected to external disturbances and its parameters undergo sudden changes in the process of mathematical modeling,the neutral stochastic functional differential equation with Markovian switching can be used to describe the realistic system.Since its exact solution is difficult to be expressed,its numerical solution is often used in numerical simulation.Due to the simultaneous presence of the neutral term and Markovian switching,investigating the numerical solution of the neutral stochastic functional differential equation with Markov switching will encounter a bottleneck.In this thesis,we mainly consider the stability and convergence of the Euler-Maruyama numerical solution of neutral stochastic functional differential equation with Markovian switching.The organization of this thesis is given as follows:In the first Chapter,we mainly introduce the research background at home and abroad,the main innovation points of this paper,give the theoretical knowledge of random analysis and basic inequalities used in this thesis,as well as some commonly used symbols.In the second Chapter,the strong convergence for the tamed Euler-Maruyama numerical solution of neutral stochastic functional differential equation is analyzed when the drift term and the dissipation term satisfy local Lipschitz condition and local monotonicity condition,and the neutral term satisfies the constractive condition.In addition,when the global Lipschitz condition and the global monotonicity condition satisfied,the strong convergence and the order of convergence of the tamed Euler-Maruyama numerical solution are also considered.In the third Chapter,the stability in distribution and strong convergence of theEuler-Maruyama numerical solution of neutral stochastic functional differential equation with Markovian switching are analyzed when the drift term and the dissipation term satisfy the global Lipschitz condition and the global monotonicity condition,and the neutral term satisfies the constractive condition.