TY - JOUR

T1 - Noise suppresses exponential growth under
regime switching

AU - Mao, X.

AU - Hu, G.

AU - Liu, M.

AU - Song, M.

AU - National Natural Science Foundation of China (Funder)

AU - London Mathematical Society (Funder)

AU - Royal Society of Edinburgh (Funder)

AU - Harbin Institute of Technology (Funder)

AU - University of Science and Technology Beijing (Funder)

PY - 2009/7/15

Y1 - 2009/7/15

N2 - 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.

AB - 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.

KW - Brownian motion

KW - Markov chain

KW - stochastic dierential equation

KW - stochastic control

KW - exponential growth

KW - polynomial growth.

UR - http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WK2-4VKXC99-4&_user=875629&_rdoc=1&_fmt=&_orig=search&_sort=d&_docanchor=&view=c&_acct=C000046979&_version=1&_urlVersion=0&_userid=875629&md5=3397c4b158a0032caddcce3d7bd366d5

UR - http://dx.doi.org/10.1016/j.jmaa.2009.02.009

U2 - 10.1016/j.jmaa.2009.02.009

DO - 10.1016/j.jmaa.2009.02.009

M3 - Article

VL - 355

SP - 783

EP - 795

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 2

ER -