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Noise expresses exponential growth under regime switching. (English) Zbl 1184.93027
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:
93B12Variable structure systems
93E03General theory of stochastic systems
60H15Stochastic partial differential equations
60G22Fractional processes, including fractional Brownian motion
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