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
SN - 0022-247X
VL - 355
SP - 783
EP - 795
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 2
ER -