中文摘要：

提出了一种新类型的随机微分方程,即具有自激发转换的随机微分方程,给出了这类方程的应用背景,研究了随机方程的一种重要的稳定性——依分布稳定性.这种稳定性可以很好地反应系统长期发展变化的统计规律,指出了研究这类随机稳定性的必要性,给出了依分布稳定性的充分条件.引入了Monte Carlo随机模拟办法、模拟系统的不变概率分布,对具体的例子给出了方程不变概率分布的数值模拟结果.

英文摘要：

A new kind of stochastic differential equations is proposed.The stochastic differential equation with self-exciting switching,and the application background of this kind of equation are presented in details.An important stability in distribution is investigated.This kind of stability can reflect the long-term statistical behaviour of a system and the necessity to study this kind of stability is also explained.Some sufficient conditions which can guarantee stability in distribution are obtained.By introducing the method of Monte Carlo stochastic simulation,numerical simulation results for an example are shown so as to support the theoretical result.