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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Lyapunov exponent estimates of a class of higher-order stochastic Anderson models
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by Dan Tang and Lijun Bo PDF
Proc. Amer. Math. Soc. 136 (2008), 4033-4043 Request permission

Abstract:

In this article, we propose a class of high-order stochastic partial differential equations (SPDEs) for spatial dimensions $d\leq 5$ 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
  • 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
  • © 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), 4033-4043
  • MSC (2000): Primary 60H15, 34A34, 49N60
  • DOI: https://doi.org/10.1090/S0002-9939-08-09442-2
  • MathSciNet review: 2425745