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Annealed large deviations for diffusions in a random Gaussian shear flow drift. (English) Zbl 1051.60028
Summary: We prove a full large deviations principle for the one-dimensional laws of the diffusion process with random drift \(X^{\varepsilon }_t = \varepsilon ^{2/3}W_t + \varepsilon ^{1/3}\int ^t_0 V(X^{\varepsilon }_s/\varepsilon )\,ds\), where \(V\) is a centered Gaussian shear flow random field independent of the Brownian \(W\). The large deviations principle is an annealed one, that is integrated over the randomnesses of \(V\) and \(W\).

60F10 Large deviations
60G10 Stationary stochastic processes
Full Text: DOI
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