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

 

Lyapunov exponent estimates of a class of higher-order stochastic Anderson models


Authors: Dan Tang and Lijun Bo
Journal: Proc. Amer. Math. Soc. 136 (2008), 4033-4043
MSC (2000): Primary 60H15, 34A34, 49N60
Published electronically: June 5, 2008
MathSciNet review: 2425745
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Abstract | References | Similar Articles | Additional Information

Abstract: In this article, we propose a class of high-order stochastic partial differential equations (SPDEs) for spatial dimensions $ d\leq5$ which might be called high-order stochastic Anderson models. This class of the equations is perturbed by a space-time white noise when $ d\leq 3$ and by a space-correlated Gaussian noise when $ d=4,5$. The objectives of this article are to get some estimates on the Lyapunov exponent of the solutions and to study the convergence rates of the chaos expansions of the solutions for the models.


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Additional Information

Dan Tang
Affiliation: School of Mathematical Sciences, Nankai University, Tianjin 300071, People’s Republic of China
Email: dantangcn@yahoo.com.cn

Lijun Bo
Affiliation: Department of Mathematics, Xidian University, Xi’an 710071, People’s Republic of China
Email: bolijunnk@yahoo.com.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09442-2
PII: S 0002-9939(08)09442-2
Keywords: High-order SPDEs, stochastic Anderson models, Lyapunov exponent, convergence rates.
Received by editor(s): October 18, 2007
Published electronically: June 5, 2008
Additional Notes: This work was supported by the LPMC at Nankai University and the NSF of China (No. 10471003).
Communicated by: Edward C. Waymire
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.