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Zbl 1184.93027
Hu, Guangda; Liu, Mingzhu; Mao, Xuerong; Song, Minghui
Noise expresses exponential growth under regime switching. (English)
[J] Syst. Control Lett. 58, No. 9, 691-699 (2009). ISSN 0167-6911

Summary: Consider a given system under regime switching whose solution grows at most polynomially, and suppose that the system is subject to environmental noise in some regimes. Can regime switching and the environmental noise work together to make the system change significantly? The answer is yes. In this paper, we will show that the regime switching and the environmental noise will make the original system whose solution grows at most polynomially become a new system whose solution will grow exponentially. In other words, we reveal that regime switching and the environmental noise will express the exponential growth.

MSC 2000:: *93B12 Variable structure systems
93E03 General theory of stochastic systems
60H15 Stochastic partial differential equations
60G22

Keywords: Brownian motion; Markov chain; stochastic differential equation; stochastic perturbation; exponential growth; polynomial growth

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