LDP and CLT for SPDEs with transport noise

Stochastics and Partial Differential Equations: Analysis and Computations(2024)

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摘要
In this work we consider solutions to stochastic partial differential equations with transport noise, which are known to converge, in a suitable scaling limit, to solution of the corresponding deterministic PDE with an additional viscosity term. Large deviations and Gaussian fluctuations underlying such scaling limit are investigated in two cases of interest: stochastic linear transport equations in dimension D≥ 2 and 2D Euler equations in vorticity form. In both cases, a central limit theorem with strong convergence and explicit rate is established. The proofs rely on nontrivial tools, like the solvability of transport equations with supercritical coefficients and Γ -convergence arguments.
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关键词
Large deviation principle,Central limit theorem,Transport noise,Stochastic transport equation,Stochastic 2D Euler equation
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