Practical Stability Analysis Of Two Kinds Of Stochastic Differential Equations With General Decay Rates

This dissertation mainly studies the almost sure practical stability of two kinds of stochastic differential equations with general decay rates.As is known to all,stability,as an important subject of stochastic differential equations,is always a classic research direction.In this paper,based on the proper Lyapunov function,we obtain sufficient conditions to guarantee the practical stability of stochastic differential systems by using stochastic analysis theory,exponential martingale inequality and Borel-Cantelli theorem,etc.Finally,we give some examples to prove the validity of the results.This paper is divided into five chapters.The first chapter introduces the basic contents of stochastic differential equations with Markov switching and L(?)vy noisedriven stochastic differential equations and the current state of research on the stability of these two types of stochastic differential equations,and also gives the basic contents of practical stability.The second chapter and the third chapter are the main innovations of this paper.The second chapter investigates the sufficient conditions for the almost sure practical asymptotic stability of stochastic differential equations with Markov switching,and also obtains two corollaries for the almost sure asymptotic stability of the system,and the conditions of these two corollaries are also general.In the third chapter,sufficient conditions are given for the L(?)vy noisedriven stochastic differential equations to guarantee almost sure practical asymptotic stability.The fourth chapter gives three examples to verify the applicability of the above theorems.The fifth chapter gives a brief summary of the paper and an outlook for the future.The end of this dissertation includes some references,a brief introduction of the author,the paper of the author published and thanks.