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

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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},
     publisher = {mathdoc},
     volume = {64},
     number = {2},
     year = {1989},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1989_64_2_a14/}
}
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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/