The Stability Of Stochastic Differential Equations

Currently,stochastic differential equations have rapidly and extensively penetrated into many fields of natural sciences and engineering technology.In view of the wide applicability of stochastic differential equations,this thesis organizes them into a book report after understanding the relevant contents.It will briefly introduce the theory of stability of stochastic differential equations and stabilize some typical stochastic differential equations.Some discussions made everyone have more knowledge of this emerging subject and facilitated further research.First of all,this thesis makes a basic introduction to the knowledge of probability theory.From basic probabilistic space to stochastic process basic knowledge and Kolmogorov theorem,it lays a foundation for elaborating the stability of stochastic differential equations.Secondly,the definition of solution for deterministic and stochastic dissipative differential equations is given,and the existence and uniqueness theorems are given under certain conditions.The stability of the solutions of stochastic differential equations in the sense of probability is further analyzed.Finally,based on the above knowledge,the stability of differential equations under stochastic perturbation is further analyzed,and a more abundant conclusion of Gaussian process is given,and the above results are applied to the linear system.