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Noise suppresses exponential growth under regime switching. (English) Zbl 1173.60024
Authors’ abstract: Consider a given system under regime switching whose solution grows exponentially, 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 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 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 supress the exponential growth.
MSC:
60H30Applications of stochastic analysis
60J65Brownian motion
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