解的依概率稳定性结果的一些推广

Some Generalizations of the Stability of the Solutions to Stochastic Differential Equations

一直以来,确定性微分方程在很多科学研究中发挥着相当重要的作用,但事物所处的环境不可避免地会存在一些偶然的、随机的因素,其中很多因素会影响系统状态的变化.如果研究人员建模时对精度要求不高,或者仅希望研究其大致的运动特征,完全可以忽略这些随机因素,以便简化模型.但有些时候,随机因素会对事物运动的本质产生影响,这样就有必要对其加以考虑,否则建模就不能做到准确描述实际情况.主要研究了随机微分方程解的稳定性在推广系数之后的情况.先将经典的随机微分方程的系数部分进行推广,之后对这一类新方程进行讨论.得到了相应的随机微分方程的解的定义和依概率稳定性的结果.

Deterministic differential equations have always played a very important role in many scientific researches,but there are some accidental and random factors in the environment in which things are located,many of which will have an impact on the state of the system.If the researchers does not require high precision,or only wants to study its general motion characteristics.These random factors can be neglected to simplify the model.But sometimes,random factors will affect the nature of motion,so it is necessary to considering,otherwise modeling will not accurately describe the actual situation.The stability of the solution of stochastic differential equations after the generalization coefficient is studied in this paper.Firstly,the coefficient part of the classical stochastic differential equation is generalized.The new class equations are discussed.The definitions of the corresponding stochastic differential equations and the results of probability stability are obtained.