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Large deviation principle and inviscid shell models
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Bessaih, H, Millet, A. (2009). Large deviation principle and inviscid shell models .
14 2551-2579. 10.1214/EJP.v14-719
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Bessaih, H, Millet, A. (2009). Large deviation principle and inviscid shell models .
14 2551-2579. 10.1214/EJP.v14-719
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cited authors
Bessaih, H; Millet, A
authors
Bessaih, Hakima
abstract
A LDP is proved for the inviscid shell model of turbulence. As the viscosity coefficient v converges to 0 and the noise intensity is multiplied by √ v, we prove that some shell models of turbulence with a multiplicative stochastic perturbation driven by a H-valued Brownian motion satisfy a LDP in C([0, T], V) for the topology of uniform convergence on [0, T], but where V is endowed with a topology weaker than the natural one. The initial condition has to belong to V and the proof is based on the weak convergence of a family of stochastic control equations. The rate function is described in terms of the solution to the inviscid equation. © 2009 Applied Probability Trust.
publication date
January 1, 2009
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Digital Object Identifier (DOI)
https://doi.org/10.1214/ejp.v14-719
Additional Document Info
start page
2551
end page
2579
volume
14