Geodesic
On the first quasiderivatives of solutions of Ito stochastic equations
Izvestiya. Mathematics , Tome 40 (1993) no. 2, pp. 377-403.

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In the study of smoothness of probabilistic solutions of differential equations an important role is played by the derivatives of the solutions of stochastic equations with respect to the initial data. In this article the possibility of replacing them by other processes called quasiderivatives is considered. As examples of the advantage of such a substitution, the intrinsic smoothness of probabilistic solutions in a domain is proved in several cases. 
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N. V. Krylov. On the first quasiderivatives of solutions of Ito stochastic equations. Izvestiya. Mathematics , Tome 40 (1993) no. 2, pp. 377-403. http://geodesic.mathdoc.fr/item/IM2_1993_40_2_a3/

[1] Krylov N. V., “Gladkost funktsii vyigrysha dlya upravlyaemogo diffuzionnogo protsessa v oblasti”, Izv. AN SSSR. Ser. matem., 53:1 (1989), 66–96 | MR

[2] Oleinik O. A., Radkevič E. V., Second order equations with nonnegative characteristic form, Plenum Press, N.Y., London, 1973 | MR

[3] Gikhman I. I., Skorokhod A. V., Stokhasticheskie differentsialnye uravneniya i ikh prilozheniya, Nauk. dumka, Kiev, 1982 | MR

[4] Vatanabe S, Ikeda N., Stokhasticheskie differentsialnye uravneniya i diffuzionnye protsessy, Nauka, M., 1986 | MR

[5] Krylov N. V., “Prostoe dokazatelstvo suschestvovaniya resheniya stokhasticheskogo uravneniya Ito s monotonnymi koeffitsientami”, Teoriya veroyatn. i ee primenen., 35:3 (1990), 1188–1192 | MR

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

[7] Gyongy I., Krylov N. V., “On stochastic equations with respect to semimartingales, I”, Stochastics, 4 (1980), 1–21 | MR

[8] Krylov N. V., “Ob otsenkakh momentov kvaziproizvodnykh reshenii stokhasticheskikh uravnenii po nachalnym dannym i ikh primenenii”, Matem. sb., 136:4 (1988), 510–529 | MR | Zbl

[9] Stroock D. W., Varadhan S. R. S., Multidimensional diffusion processes, Springer, Berlin, 1979 | MR | Zbl