Geodesic
Parabolic equations with a small parameter, and large deviations for diffusion processes
Sbornik. Mathematics, Tome 83 (1995) no. 2, pp. 331-346 Cet article a éte moissonné depuis la source Math-Net.Ru

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Nonlinear second-order parabolic equations with a small parameter at the highest derivative and coefficients depending on this parameter are considered. Under weak convergence in $L_{2,\mathrm{loc}}$ of the coefficients of the equation, uniform convergence on compacta of solutions to a generalized solution of a first-order partial differential equation is established. This result is used to justify the principle of large deviations for diffusion processes with small diffusion and coefficients that converge weakly in $L_{2,\mathrm{loc}}$. 
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S. Ya. Makhno. Parabolic equations with a small parameter, and large deviations for diffusion processes. Sbornik. Mathematics, Tome 83 (1995) no. 2, pp. 331-346. http://geodesic.mathdoc.fr/item/SM_1995_83_2_a3/

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