Almost Sure Asymptotic Stability for Regime-Switching Diffusions

Junhao Hu; Jianhai Bao; Chenggui Yuan

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arXiv · 1410.7643

Almost Sure Asymptotic Stability for Regime-Switching Diffusions

Junhao Hu·Jianhai Bao·Chenggui Yuan

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Abstract

In this paper, we discuss long-time behavior of sample paths for a wide range of regime-switching diffusions. Firstly, 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. We then apply our theory to study the stabilization for linear switching models. Several examples are given to demonstrate our theory.

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BibTeX RIS

Junhao Hu, Jianhai Bao, Chenggui Yuan. 2014-10-28. Almost Sure Asymptotic Stability for Regime-Switching Diffusions. https://arxiv.org/abs/1410.7643

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