本文選題：積分微分方程　切入點：時滯隨機微分方程　出處：《四川師范大學》2017年碩士論文　論文類型：學位論文

【摘要】：本文研究一類含時滯的隨機非線性積分微分方程的穩(wěn)定性.尋求研究時滯隨機微分方程穩(wěn)定性的新方法一直以來都是學者們重點關(guān)注的對象之一.本文首先建立該類方程的常數(shù)變易公式,得出其解的表達形式.其次使用不等式分析技巧,構(gòu)建恰當?shù)臅r滯積分不等式和指數(shù)型時滯積分不等式.最后使用隨機分析理論和不等式分析技巧,借助構(gòu)建的時滯積分不等式,建立了判別這類時滯的隨機非線性積分微分方程的p階矩穩(wěn)定、p階矩漸近穩(wěn)定、p階矩一致漸近穩(wěn)定、p階矩全局一致漸近穩(wěn)定、p階矩指數(shù)穩(wěn)定和p階矩全局指數(shù)穩(wěn)定性的充分條件(p ≥ 2).文中的舉例闡述了時滯積分不等式方法的有效性。
[Abstract]:In this paper, we study the stability of a class of stochastic nonlinear integrodifferential equations with time delay, and seek a new method to study the stability of stochastic differential equations with delay. The constant variable formula of this kind of equation, The expression form of the solution is obtained. Secondly, the appropriate delay integral inequality and exponential delay integral inequality are constructed by using the inequality analysis technique. Finally, the stochastic analysis theory and inequality analysis technique are used. With the help of the time delay integral inequality constructed, In this paper, the p order moment stability and p order moment asymptotic stability of stochastic nonlinear integrodifferential equations with such delays are established, and the global uniform asymptotic stability of p order moment and p order moment exponential stability and p order moment global exponential stability are established. The sufficient condition for qualitative analysis is p 鈮，

本文編號：1587832