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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 \(W\).

MSC:
60F10 Large deviations
60G10 Stationary stochastic processes
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