Probabilistic problems in the theory of hypoellipticity
Izvestiya. Mathematics , Tome 25 (1985) no. 3, pp. 455-473.

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

Local smoothness is established for the distribution density of a solution of an Ito–Stratonovich stochastic equation under the assumption of local smoothness condition of Hörmander. Bibliography: 20 titles.
@article{IM2_1985_25_3_a2,
     author = {A. Yu. Veretennikov},
     title = {Probabilistic problems in the theory of hypoellipticity},
     journal = {Izvestiya. Mathematics },
     pages = {455--473},
     publisher = {mathdoc},
     volume = {25},
     number = {3},
     year = {1985},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1985_25_3_a2/}
}
TY  - JOUR
AU  - A. Yu. Veretennikov
TI  - Probabilistic problems in the theory of hypoellipticity
JO  - Izvestiya. Mathematics 
PY  - 1985
SP  - 455
EP  - 473
VL  - 25
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1985_25_3_a2/
LA  - en
ID  - IM2_1985_25_3_a2
ER  - 
%0 Journal Article
%A A. Yu. Veretennikov
%T Probabilistic problems in the theory of hypoellipticity
%J Izvestiya. Mathematics 
%D 1985
%P 455-473
%V 25
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1985_25_3_a2/
%G en
%F IM2_1985_25_3_a2
A. Yu. Veretennikov. Probabilistic problems in the theory of hypoellipticity. Izvestiya. Mathematics , Tome 25 (1985) no. 3, pp. 455-473. http://geodesic.mathdoc.fr/item/IM2_1985_25_3_a2/

[1] Hörmander L., “Hypoelliptic second order differential equations”, Acta Mathematica, 119 (1967), 147–171 | DOI | MR | Zbl

[2] Oleinik O. A., Radkevich E. V., “Uravneniya vtorogo poryadka s neotritsatelnoi kharakteristicheskoi formoi”, Itogi nauki, seriya matem., 22, VINITI, M., 1971, 252 | MR

[3] Malliavin P., “Stochastic calculus of variations and hypoelliptic operators”, Proc. Internat. Conf. on Stochastic differential equations (Kyoto, 1976), Tokyo, Kinokumiya, New York, Wiley, 1978, 195–263 | MR | Zbl

[4] Malliavin P., “$C^k$-hypoellipticity with degeneracy”, Stochastic Analysis, eds. A. Friedman, M. Pinsky, Acad. Press, New York, London, 1978, 199–214 | MR

[5] Strook D. W., “The Malliavin calculus and its applications”, Lecture Notes in Math., 851, 1981, 394–432 | MR

[6] Strook D. W., “The Malliavin calculus and its application to second order parabolic differential equations, I, II”, Math. System Theory, 14 (1981), 25–65 ; 2, 141–171 | DOI | MR

[7] Strook D. W., “The Malliavin calculus, a functional analytic approach”, J. Functional Anal., 44 (1981), 212–257 | DOI | MR

[8] Bismut J. M., “Martingales, the Malliavin calculus and Hörmander's theorem”, Lecture Notes in Math., 851, 1981, 85–109 | MR | Zbl

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

[10] Bismut J. M., Michel D., “Diffusions conditionnelles. I: Hypoellipticité partielle”, J. Functional Anal., 44 (1981), 174–211 ; “II: Generateur Conditionnell. Application an filtrage”, J. Functional Anal., 45 (1982), 274–292 | DOI | MR | Zbl | DOI | MR | Zbl

[11] Ikeda N., Watanabe S., Stochastic differential equations and diffusion processes, North-Holland Publ. Co., Tokyo, Kodansha, New York, Oxford, Amsterdam, 1981, 464 | MR | Zbl

[12] Ichihara K., Kunita H., “A classification of second order degenerate elliptie operators and its probabilistic characterization”, Z. Wahrsch., 30 (1974), 235–254 | DOI | MR | Zbl

[13] Krylov N. V., Rozovskii B. L., “Stokhasticheskie uravneniya v chastnykh proizvodnykh i diffuzionnye protsessy”, Uspekhi matem. nauk, 37:6 (1982), 75–95 | MR | Zbl

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

[15] Gikhman I. I., Skorokhod A. V., Stokhasticheskie differentsialnye uravneniya, Naukova dumka, Kiev., 1968 | Zbl

[16] Dub Dzh. L., Veroyatnostnye protsessy, IL, M., 1956, 606

[17] Liptser R. Sh., Shiryaev A. N., Statistika sluchainykh protsessov, Nauka, M., 1974, 696 | MR | Zbl

[18] Danford H., Shvarts Dzh. T., Lineinye operatory. Obschaya teoriya, IL, M., 1962, 896

[19] Venttsel A. D., Kurs teorii sluchainykh protsessov, Nauka, M., 1975, 320 | MR

[20] Landis E. M., Uravneniya vtorogo poryadka ellipticheskogo i parabolicheskogo tipov, Nauka, M., 1971, 288 | MR