IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v142y2021icp159-194.html
   My bibliography  Save this article

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

Author

Listed:
  • 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.

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414921001423
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2021.08.010?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Cardon-Weber, Caroline, 1999. "Large deviations for a Burgers'-type SPDE," Stochastic Processes and their Applications, Elsevier, vol. 84(1), pages 53-70, November.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Deugoué, G. & Tachim Medjo, T., 2023. "Large deviation for a 3D globally modified Cahn–Hilliard–Navier–Stokes model under random influences," Stochastic Processes and their Applications, Elsevier, vol. 160(C), pages 33-71.
    2. 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.
    3. 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.
    4. Swie[combining cedilla]ch, Andrzej, 2009. "A PDE approach to large deviations in Hilbert spaces," Stochastic Processes and their Applications, Elsevier, vol. 119(4), pages 1081-1123, April.
    5. Budhiraja, Amarjit & Chen, Jiang & Dupuis, Paul, 2013. "Large deviations for stochastic partial differential equations driven by a Poisson random measure," Stochastic Processes and their Applications, Elsevier, vol. 123(2), pages 523-560.
    6. Ganguly, Arnab, 2018. "Large deviation principle for stochastic integrals and stochastic differential equations driven by infinite-dimensional semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 128(7), pages 2179-2227.
    7. Leila Setayeshgar, 2023. "Uniform large deviations for a class of semilinear stochastic partial differential equations driven by a Brownian sheet," Partial Differential Equations and Applications, Springer, vol. 4(1), pages 1-12, February.
    8. Pappalettera, Umberto, 2022. "Large deviations for stochastic equations in Hilbert spaces with non-Lipschitz drift," Stochastic Processes and their Applications, Elsevier, vol. 153(C), pages 1-20.
    9. 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.
    10. Cai, Yujie & Huang, Jianhui & Maroulas, Vasileios, 2015. "Large deviations of mean-field stochastic differential equations with jumps," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 1-9.
    11. Maroulas, Vasileios & Xiong, Jie, 2013. "Large deviations for optimal filtering with fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 123(6), pages 2340-2352.
    12. Maroulas, Vasileios & Pan, Xiaoyang & Xiong, Jie, 2020. "Large deviations for the optimal filter of nonlinear dynamical systems driven by Lévy noise," Stochastic Processes and their Applications, Elsevier, vol. 130(1), pages 203-231.
    13. Meng, Lixin & Li, Jingyu & Tao, Jian, 2017. "Global energy solutions to a stochastic Schrödinger–Poisson system with multiplicative noise in two dimensions," Applied Mathematics and Computation, Elsevier, vol. 300(C), pages 40-59.
    14. Hakima Bessaih & Annie Millet, 2022. "Speed of Convergence of Time Euler Schemes for a Stochastic 2D Boussinesq Model," Mathematics, MDPI, vol. 10(22), pages 1-39, November.
    15. Yang, Xue & Zhang, Qi & Zhang, Tusheng, 2020. "Reflected backward stochastic partial differential equations in a convex domain," Stochastic Processes and their Applications, Elsevier, vol. 130(10), pages 6038-6063.
    16. Chen, Chuchu & Dang, Tonghe & Hong, Jialin, 2024. "An adaptive time-stepping fully discrete scheme for stochastic NLS equation: Strong convergence and numerical asymptotics," Stochastic Processes and their Applications, Elsevier, vol. 173(C).
    17. Zhang, Tusheng, 2012. "Large deviations for invariant measures of SPDEs with two reflecting walls," Stochastic Processes and their Applications, Elsevier, vol. 122(10), pages 3425-3444.
    18. Röckner, Michael & Zhu, Rongchan & Zhu, Xiangchan, 2014. "Local existence and non-explosion of solutions for stochastic fractional partial differential equations driven by multiplicative noise," Stochastic Processes and their Applications, Elsevier, vol. 124(5), pages 1974-2002.
    19. Li, Ruinan & Li, Yumeng, 2020. "Talagrand’s quadratic transportation cost inequalities for reflected SPDEs driven by space–time white noise," Statistics & Probability Letters, Elsevier, vol. 161(C).
    20. Mohan, Manil T., 2020. "Well posedness, large deviations and ergodicity of the stochastic 2D Oldroyd model of order one," Stochastic Processes and their Applications, Elsevier, vol. 130(8), pages 4513-4562.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:142:y:2021:i:c:p:159-194. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.