Geodesic
On approximation of Itô stochastic equations
Sbornik. Mathematics, Tome 70 (1991) no. 1, pp. 165-173 
I. Gyöngy. On approximation of Itô stochastic equations. Sbornik. Mathematics, Tome 70 (1991) no. 1, pp. 165-173. http://geodesic.mathdoc.fr/item/SM_1991_70_1_a10/
@article{SM_1991_70_1_a10,
     author = {I. Gy\"ongy},
     title = {On approximation of {It\^o} stochastic equations},
     journal = {Sbornik. Mathematics},
     pages = {165--173},
     year = {1991},
     volume = {70},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1991_70_1_a10/}
}
TY  - JOUR
AU  - I. Gyöngy
TI  - On approximation of Itô stochastic equations
JO  - Sbornik. Mathematics
PY  - 1991
SP  - 165
EP  - 173
VL  - 70
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SM_1991_70_1_a10/
LA  - en
ID  - SM_1991_70_1_a10
ER  - 
%0 Journal Article
%A I. Gyöngy
%T On approximation of Itô stochastic equations
%J Sbornik. Mathematics
%D 1991
%P 165-173
%V 70
%N 1
%U http://geodesic.mathdoc.fr/item/SM_1991_70_1_a10/
%G en
%F SM_1991_70_1_a10

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

Under relaxed conditions on the coefficients, an approximation to the solution of stochastic differential equations with semimartingales is established, when the integrals and the coefficients appearing in the equations are approximated.

[1] Ikeda N., Nakao S., Yamato Y., “A class of approximations for Brownian motion”, Publ. RIMS. Kyoto Univ., 13 (1977), 285–300 | DOI | MR | Zbl

[2] Ikeda N., Watanabe S., Stochastic Differential Equations and Diffusion Processes, Amsterdam–Tokyo, North-Holland-Kodanska, 1981 | MR | Zbl

[3] Matskyavichyus V. K., “$S^p$-ustoichivost reshenii simmetricheskikh stokhasticheskikh uravnenii”, Litov. matem. sb., 25:4 (1985), 72–84 | MR

[4] Gyöngy I., “On the approximation of stochastic differential equations”, Stochastics, 23 (1988), 331–352 | MR | Zbl

[5] Gyöngy I., “On the approximation of stochastic partial differential equations, I”, Stochastics, 25 (1988), 59–85 | MR | Zbl

[6] Picard J., 6. Methods de perturbation pour les equations differentielles stochastiques et le filtrage non lineaire, L'Universite de Provence Centre Saint-Charles, These, 1987

[7] Mackevicius V., “$S^p$ stability of solutions of symmetric stochastic differential equations with discontinuous driwing semimartingales”, Ann. Inst. Henri Poincare, 23:4 (1987), 575–592 | MR | Zbl