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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The moment and almost surely exponential stability of stochastic heat equations


Author: Bin Xie
Journal: Proc. Amer. Math. Soc. 136 (2008), 3627-3634
MSC (2000): Primary 93D20; Secondary 60H15, 35R60
Published electronically: May 15, 2008
MathSciNet review: 2415047
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Abstract: In this article, the $ p$-th moment and almost surely exponential stability of the strong solution to a stochastic heat equation driven by an $ m$-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: http://dx.doi.org/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
Published electronically: May 15, 2008
Additional Notes: This work is supported by a scholarship of the Japanese government (Monbukagakusho).
Communicated by: Walter Craig
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.