Abstract
In this paper, we discuss long-time behavior of sample paths for a wide range of regime-switching diffusions. Almost sure asymptotic stability is concerned (i) for regime-switching diffusions with finite state spaces by the Perron-Frobenius theorem, and, with regard to the case of reversible Markov chain, via the principal eigenvalue approach; (ii) for regime-switching diffusions with countable state spaces by means of a finite partition trick and an M -Matrix theory. Moreover, we apply our theory to study the stabilization for linear switching models. Several examples are given to demonstrate our theory.
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