Geodesic
Parabolic equations with a~small parameter, and large deviations for diffusion processes
Sbornik. Mathematics, Tome 83 (1995) no. 2, pp. 331-346

Voir la notice de l'article provenant de la source Math-Net.Ru

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 $L_{2,\mathrm{loc}}$. 
@article{SM_1995_83_2_a3,
     author = {S. Ya. Makhno},
     title = {Parabolic equations with a~small parameter, and large deviations for diffusion processes},
     journal = {Sbornik. Mathematics},
     pages = {331--346},
     publisher = {mathdoc},
     volume = {83},
     number = {2},
     year = {1995},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1995_83_2_a3/}
}
TY  - JOUR
AU  - S. Ya. Makhno
TI  - Parabolic equations with a~small parameter, and large deviations for diffusion processes
JO  - Sbornik. Mathematics
PY  - 1995
SP  - 331
EP  - 346
VL  - 83
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_1995_83_2_a3/
LA  - en
ID  - SM_1995_83_2_a3
ER  - 
%0 Journal Article
%A S. Ya. Makhno
%T Parabolic equations with a~small parameter, and large deviations for diffusion processes
%J Sbornik. Mathematics
%D 1995
%P 331-346
%V 83
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_1995_83_2_a3/
%G en
%F SM_1995_83_2_a3
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/