Noise expresses exponential growth under regime switching

Guangda Hu, Mingzhu Liu, Xuerong Mao, Minghui Song, National Natural Science Foundation of China (Funder), University of Science and Technology, Beijing (Funder), Harbin Institute of Technology (Funder)

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

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 the regime switching and the environmental noise work together to make the system change signicantly? 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 the regime switching and the environmental noise will exppress the exponential growth.
LanguageEnglish
Pages691-699
Number of pages8
JournalSystems and Control Letters
Volume58
Issue number9
DOIs
Publication statusPublished - Sep 2009

Keywords

  • brownian motion
  • markov chain
  • stochastic differential equation
  • stochastic perturbation
  • exponential growth
  • polynomial growth

Cite this

Hu, G., Liu, M., Mao, X., Song, M., National Natural Science Foundation of China (Funder), University of Science and Technology, Beijing (Funder), & Harbin Institute of Technology (Funder) (2009). Noise expresses exponential growth under regime switching. Systems and Control Letters, 58(9), 691-699. https://doi.org/10.1016/j.sysconle.2009.06.006
Hu, Guangda ; Liu, Mingzhu ; Mao, Xuerong ; Song, Minghui ; National Natural Science Foundation of China (Funder) ; University of Science and Technology, Beijing (Funder) ; Harbin Institute of Technology (Funder). / Noise expresses exponential growth under regime switching. In: Systems and Control Letters. 2009 ; Vol. 58, No. 9. pp. 691-699.
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Hu, G, Liu, M, Mao, X, Song, M, National Natural Science Foundation of China (Funder), University of Science and Technology, Beijing (Funder) & Harbin Institute of Technology (Funder) 2009, 'Noise expresses exponential growth under regime switching' Systems and Control Letters, vol. 58, no. 9, pp. 691-699. https://doi.org/10.1016/j.sysconle.2009.06.006

Noise expresses exponential growth under regime switching. / Hu, Guangda; Liu, Mingzhu; Mao, Xuerong; Song, Minghui; National Natural Science Foundation of China (Funder); University of Science and Technology, Beijing (Funder); Harbin Institute of Technology (Funder).

In: Systems and Control Letters, Vol. 58, No. 9, 09.2009, p. 691-699.

Research output: Contribution to journalArticle

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AU - Hu, Guangda

AU - Liu, Mingzhu

AU - Mao, Xuerong

AU - Song, Minghui

AU - National Natural Science Foundation of China (Funder)

AU - University of Science and Technology, Beijing (Funder)

AU - Harbin Institute of Technology (Funder)

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AB - 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 the regime switching and the environmental noise work together to make the system change signicantly? 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 the regime switching and the environmental noise will exppress the exponential growth.

KW - brownian motion

KW - markov chain

KW - stochastic differential equation

KW - stochastic perturbation

KW - exponential growth

KW - polynomial growth

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Hu G, Liu M, Mao X, Song M, National Natural Science Foundation of China (Funder), University of Science and Technology, Beijing (Funder) et al. Noise expresses exponential growth under regime switching. Systems and Control Letters. 2009 Sep;58(9):691-699. https://doi.org/10.1016/j.sysconle.2009.06.006