### 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.

Original language | English |
---|---|

Pages (from-to) | 783-795 |

Number of pages | 12 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 355 |

Issue number | 2 |

DOIs | |

Publication status | Published - 15 Jul 2009 |

### Keywords

- Brownian motion
- Markov chain
- stochastic dierential equation
- stochastic control
- exponential growth
- polynomial growth.

## Cite this

Mao, X., Hu, G., Liu, M., 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), 783-795. https://doi.org/10.1016/j.jmaa.2009.02.009