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Systems of small-noise stochastic reaction–diffusion equations satisfy a large deviations principle that is uniform over all initial data

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  • Salins, M.

Abstract

Large deviations principles characterize the exponential decay rates of the probabilities of rare events. Cerrai and Röckner (2004) proved that systems of stochastic reaction–diffusion equations satisfy a large deviations principle that is uniform over bounded sets of initial data.

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  • Salins, M., 2021. "Systems of small-noise stochastic reaction–diffusion equations satisfy a large deviations principle that is uniform over all initial data," Stochastic Processes and their Applications, Elsevier, vol. 142(C), pages 159-194.
    • Handle: RePEc:eee:spapps:v:142:y:2021:i:c:p:159-194
    DOI: 10.1016/j.spa.2021.08.010
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    References listed on IDEAS

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    1. Foondun, Mohammud & Setayeshgar, Leila, 2017. "Large deviations for a class of semilinear stochastic partial differential equations," Statistics & Probability Letters, Elsevier, vol. 121(C), pages 143-151.
    2. Xu, Tiange & Zhang, Tusheng, 2009. "White noise driven SPDEs with reflection: Existence, uniqueness and large deviation principles," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3453-3470, October.
    3. Liu, Wei & Röckner, Michael & Zhu, Xiang-Chan, 2013. "Large deviation principles for the stochastic quasi-geostrophic equations," Stochastic Processes and their Applications, Elsevier, vol. 123(8), pages 3299-3327.
    4. Biswas, Anup & Budhiraja, Amarjit, 2011. "Exit time and invariant measure asymptotics for small noise constrained diffusions," Stochastic Processes and their Applications, Elsevier, vol. 121(5), pages 899-924.
    5. Gautier, Eric, 2005. "Uniform large deviations for the nonlinear Schrodinger equation with multiplicative noise," Stochastic Processes and their Applications, Elsevier, vol. 115(12), pages 1904-1927, December.
    6. Duan, Jinqiao & Millet, Annie, 2009. "Large deviations for the Boussinesq equations under random influences," Stochastic Processes and their Applications, Elsevier, vol. 119(6), pages 2052-2081, June.
    7. Sritharan, S.S. & Sundar, P., 2006. "Large deviations for the two-dimensional Navier-Stokes equations with multiplicative noise," Stochastic Processes and their Applications, Elsevier, vol. 116(11), pages 1636-1659, November.
    8. Chenal, Fabien & Millet, Annie, 1997. "Uniform large deviations for parabolic SPDEs and applications," Stochastic Processes and their Applications, Elsevier, vol. 72(2), pages 161-186, December.
    9. Cardon-Weber, Caroline, 1999. "Large deviations for a Burgers'-type SPDE," Stochastic Processes and their Applications, Elsevier, vol. 84(1), pages 53-70, November.
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    Cited by:

    1. Yue Li & Shijie Shang & Jianliang Zhai, 2024. "Large Deviation Principle for Stochastic Reaction–Diffusion Equations with Superlinear Drift on $$\mathbb {R}$$ R Driven by Space–Time White Noise," Journal of Theoretical Probability, Springer, vol. 37(4), pages 3496-3539, November.

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