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Large deviations for stochastic equations in Hilbert spaces with non-Lipschitz drift

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  • Pappalettera, Umberto

Abstract

We prove a Freidlin–Wentzell result for stochastic differential equations in infinite-dimensional Hilbert spaces perturbed by a cylindrical Wiener process. We do not assume the drift to be Lipschitz continuous, but only continuous with at most linear growth. Our result applies, in particular, to a large class of nonlinear fractional diffusion equations perturbed by a space–time white noise.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:153:y:2022:i:c:p:1-20
    DOI: 10.1016/j.spa.2022.07.004
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    References listed on IDEAS

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    1. Cardon-Weber, Caroline, 1999. "Large deviations for a Burgers'-type SPDE," Stochastic Processes and their Applications, Elsevier, vol. 84(1), pages 53-70, November.
    2. G. Prato & F. Flandoli & E. Priola & M. Röckner, 2015. "Strong Uniqueness for Stochastic Evolution Equations with Unbounded Measurable Drift Term," Journal of Theoretical Probability, Springer, vol. 28(4), pages 1571-1600, December.
    3. 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.
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