The Stability Of Stochastic Differential Equations Under Two Types Of Nonlinear Growth Conditions

With the globalization of science and information technology,people put forward higher requirements for the stability of stochastic systems in life,which makes the research on the stability of stochastic systems more and more important.Because the future development of the system depends on the past state and the present state,the neutral stochastic differential equation has been mentioned and studied by more and more scholars at home and abroad,the stability and feasibility of the real system can be described by studying the stability of its solution.The traditional linear growth conditions have many limitations on characterizing complex and diverse systems,so it is necessary to study stochastic differential systems with neutral type under highly nonlinear growth conditions.Based on neutral stochastic differential equations,this paper mainly studies the existence,uniqueness and stability of global solutions for hybrid stochastic differential equations under high nonlinear conditions.In order to overcome the interference caused by neutral type,the neutral type partially is required to satisfy the contraction mapping condition and a stopping time method is constructed in this paper.The existence and uniqueness of the global solution is proved by using the Lyapunov function.In addition,the stability of the system solution is obtained with inequality techniques.The specific content of the paper is as follows:In Chapter 1,the research background,significance,and the main innovation and some symbols in this paper are introduced.In Chapter 2,the existence,uniqueness and -th moment stability of solutions for neutral stochastic delay differential system is studied under highly nonlinear growth conditions.In order to overcome the interference caused by the term under highly nonlinear growth conditions,this paper uses inequality scaling techniques to handle the impact of the neutral term.Unlike the traditional linear growth conditions,the diffusion and drift terms in the equations in this section are nonlinear,which greatly expands the range of use of the system.In Chapter 3,the -th moment global stability in probability for the solution of the neutral stochastic differential system with Markov switching under the highly nonlinear growth condition is studied.In this paper,the linear conditions of the diffusion term and the drift term in the existing literature are improved.Also,the sufficient condition for the stability of the system solution is obtained by using the average dwell time method and Chebyshev inequality.In Chapter 4,the research results of this paper is concluded,and some directions for future researches are given.