Large deviations for a fractional stochastic heat equation in spatial dimension ℝd driven by a spatially correlated noise

DOI10.1142/S0219493716500015zbMath1331.60052arXiv1401.2798MaRDI QIDQ3465650

Tarik El Mellali, Mohamed Mellouk

Publication date: 22 January 2016

Published in: Stochastics and Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1401.2798

zbMATH Keywords

Fourier transformlarge deviations principlestochastic partial differential equationweak convergence methodfractional derivative operatorcorrelated Gaussian noise

Mathematics Subject Classification ID

Gaussian processes (60G15) Central limit and other weak theorems (60F05) Large deviations (60F10) Stochastic partial differential equations (aspects of stochastic analysis) (60H15)

Related Items (8)

Large deviations for a stochastic Cahn–Hilliard equation in Hölder norm ⋮ ON A SEMILINEAR DOUBLE FRACTIONAL HEAT EQUATION DRIVEN BY FRACTIONAL BROWNIAN SHEET ⋮ Moderate deviations for stochastic heat equation with rough dependence in Space ⋮ Moderate deviations for stochastic fractional heat equation driven by fractional noise ⋮ Large deviation principle for a space-time fractional stochastic heat equation with fractional noise ⋮ Central limit theorem for a fractional stochastic heat equation with spatially correlated noise ⋮ Moderate deviations for a class of semilinear SPDE with fractional noises ⋮ Moderate deviations for a fractional stochastic heat equation with spatially correlated noise

Cites Work

• Stochastic integrals for SPDEs: a comparison
• On the martingale problem for generators of stable processes with perturbations
• Fractional SPDEs driven by spatially correlated noise: existence of the solution and smoothness of its density
• Explicit solutions of some fractional partial differential equations via stable subordinators
• Large deviations for the Boussinesq equations under random influences
• Large deviations techniques and applications.
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