中文摘要：

这个工作涉及切换的散开过程，也已知的切换 asregime 散开。我们的注意集中于内在的随机的过程的整齐，复发，和积极复发。主要努力被奉献给为上述的性质获得容易可证实的条件。Continuous-state-dependent 跳过程被考虑。用 Liapunov 功能的整齐和复发上的第一个一般标准被获得。然后，我们集中于问题，飘移和散开系数关于连续状态在是“ linearizable ”的一个类，并且假定这进程的jump 部分的生成器能被各态历经的 Markov chain.Sufficient 的一个生成器接近为整齐的条件，复发，和积极复发被导出，它是平均系数的线性联合(关于 Markov 链的静止措施平均)。

英文摘要：

This work is concerned with switching diffusion processes, also known as regime-switching diffusions. Our attention focuses on regularity, recurrence, and positive recurrence of the underlying stochastic processes. The main effort is devoted to obtaining easily verifiable conditions for the aforementioned properties. Continuous-state-dependent jump processes are considered. First general criteria on regularity and recurrence using Liapunov functions are obtained. Then we focus on a class of problems, in which both the drift and the diffusion coefficients are ＂linearizable＂ with respect to the continuous state, and suppose that the generator of the jump part of the process can be approximated by a generator of an ergodic Markov chain. Sufficient conditions for regularity, recurrence, and positive recurrence are derived, which are linear combination of the averaged coefficients （averaged with respect to the stationary measure of the Markov chain）.