The moment and almost surely exponential stability of stochastic heat equations
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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.References
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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
- 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
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 3627-3634
- MSC (2000): Primary 93D20; Secondary 60H15, 35R60
- DOI: https://doi.org/10.1090/S0002-9939-08-09458-6
- MathSciNet review: 2415047