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The moment and almost surely exponential stability of stochastic heat equations
Author(s):
Bin
Xie
Journal:
Proc. Amer. Math. Soc.
136
(2008),
3627-3634.
MSC (2000):
Primary 93D20;
Secondary 60H15, 35R60
Posted:
May 15, 2008
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Abstract:
In this article, the  -th moment and almost surely exponential stability of the strong solution to a stochastic heat equation driven by an  -dimensional Brownian motion is investigated by a simple method. In particular, the sharp top Lyapunov exponents are explicitly calculated based on the representation of the strong solution.
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Additional Information:
Bin
Xie
Affiliation:
Graduate School of Mathematical Sciences, The University of Tokyo, Komaba, Tokyo 153-8914, Japan
Address at time of publication:
International Young Researchers Empowerment Center, and Department of Mathematical Sciences, Faculty of Science, Shinshu University, 3-1-1 Asahi, Matsumoto, Nagano 390-8621, Japan
Email:
bxie05@sohu.com, bxie@shinshu-u.ac.jp
DOI:
10.1090/S0002-9939-08-09458-6
PII:
S 0002-9939(08)09458-6
Keywords:
Stochastic heat equation,
exponential stability,
$p$-th moment,
almost surely,
Lyapunov exponent
Received by editor(s):
August 27, 2007
Posted:
May 15, 2008
Additional Notes:
This work is supported by a scholarship of the Japanese government (Monbukagakusho).
Communicated by:
Walter Craig
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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