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Noise suppresses exponential growth under regime switching

Mao, X. and Hu, G. and Liu, M. and Song, M., National Natural Science Foundation of China (Funder), London Mathematical Society (Funder), Royal Society of Edinburgh (Funder), Harbin Institute of Technology. (Funder), University of Science and Technology Beijing (Funder) (2009) Noise suppresses exponential growth under regime switching. Journal of Mathematical Analysis and Applications, 355 (2). pp. 783-795. ISSN 0022-247X

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Abstract

Consider a given system under regime switching whose solution grows expo- nentially, 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 exponentially become a new system whose solutions will grow at most polynomially. In other words, we reveal that the regime switching and the environmental noise will suppress the exponential growth.