Abstract：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.

Keyword：stability in distribution;equilibrium solution;self-exciting switching;