Geodesic
On moment estimates for quasiderivative of solutions of stochastic equations with respect to the initial data, and their applications
Sbornik. Mathematics, Tome 64 (1989) no. 2, pp. 505-526 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

There is a well-known method for proving smoothness of a probabilistic solution of an elliptic equation in space, based on studying the growth as $t\to\infty$ of the moments of the derivatives with respect to the initial data of a solution of an Ito stochastic equation. This article introduces the concept of quasiderivatives, which “work” in the places where derivatives work, and which enable one to essentially weaken the known conditions ensuring smoothness of a probabilistic solution of an elliptic equation. Bibliography: 12 titles. 
@article{SM_1989_64_2_a14,
     author = {N. V. Krylov},
     title = {On moment estimates for quasiderivative of solutions of stochastic equations with respect to the initial data, and their applications},
     journal = {Sbornik. Mathematics},
     pages = {505--526},
     year = {1989},
     volume = {64},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1989_64_2_a14/}
}
TY  - JOUR
AU  - N. V. Krylov
TI  - On moment estimates for quasiderivative of solutions of stochastic equations with respect to the initial data, and their applications
JO  - Sbornik. Mathematics
PY  - 1989
SP  - 505
EP  - 526
VL  - 64
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1989_64_2_a14/
LA  - en
ID  - SM_1989_64_2_a14
ER  - 
%0 Journal Article
%A N. V. Krylov
%T On moment estimates for quasiderivative of solutions of stochastic equations with respect to the initial data, and their applications
%J Sbornik. Mathematics
%D 1989
%P 505-526
%V 64
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1989_64_2_a14/
%G en
%F SM_1989_64_2_a14
N. V. Krylov. On moment estimates for quasiderivative of solutions of stochastic equations with respect to the initial data, and their applications. Sbornik. Mathematics, Tome 64 (1989) no. 2, pp. 505-526. http://geodesic.mathdoc.fr/item/SM_1989_64_2_a14/

[1] Gikhman I. I., “K teorii differentsialnykh uravnenii sluchainykh protsessov. I, II”, Ukr. matem. zhurn., 2:4 (1950), 37–63 ; 3:3 (1951), 317–339 | MR | MR

[2] Blagoveschenskii Yu. N., Freidlin M. I., “Nekotorye svoistva diffuzionnykh protsessov, zavisyaschikh ot parametra”, DAN SSSR, 138:3 (1961), 508–511 | MR | Zbl

[3] Freidlin M. I., “O gladkosti reshenii vyrozhdayuschikhsya ellipticheskikh uravnenii”, Izv. AN SSSR. Ser. matem., 32:6 (1968), 1391–1413 | MR | Zbl

[4] Krylov N. V., Upravlyaemye protsessy diffuzionnogo tipa, Nauka, M., 1977 | MR

[5] Krylov N. V., “Ob upravlenii diffuzionnym protsessom do momenta pervogo vykhoda iz oblasti”, Izv. AN SSSR. Ser. matem., 45 (1981), 1029–2048 | MR

[6] Hausman U., “On the integral representation of functionals of Ito processes”, Stochastics, 3 (1979), 17–27 | MR

[7] Bismut J. M., “Martingales, the Malliavin calculus and hypoellipticity under general Hörmander's conditions”, Z. Wahrsch, 56 (1981), 469–505 | DOI | MR | Zbl

[8] Krylov N. V., “O bezuslovnoi razreshimosti uravneniya Bellmana s postoyannymi koeffitsientami v vypuklykh oblastyakh”, Matem. sb., 135(177) (1988), 297–311 | MR | Zbl

[9] Liptser R. Sh., Shiryaev A. N., Teoriya martingalov, Nauka, M., 1987 | MR

[10] Dellasheri K., Emkosti i sluchainye protsessy, Mir, M., 1975 | MR

[11] Krylov N. V., Nelineinye ellipticheskie i parabolicheskie uravneniya vtorogo poryadka, Nauka, M., 1975 | MR

[12] Pardoux E., Equations aux dérivées partielles stochastiques non lineaires monotones, Thes. P., 1975 | Zbl