Almost Sure Asymptotic Stability for Regime-Switching Diffusions

2014/10/28 by Junhao Hu, Hu, Junhao, Jianhai Bao +3
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · #Gene Regulatory Network Analysis #Neural Networks Stability and Synchronization #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1410.7643

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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