This article is cited in 4 scientific papers (total in 4 papers)
On moment estimates for quasiderivative of solutions of stochastic equations with respect to the initial data, and their applications
N. V. Krylov
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.
PDF file (1115 kB)
Mathematics of the USSR-Sbornik, 1989, 64:2, 505–526
MSC: 60H10, 60H15
N. V. Krylov, “On moment estimates for quasiderivative of solutions of stochastic equations with respect to the initial data, and their applications”, Mat. Sb. (N.S.), 136(178):4(8) (1988), 510–529; Math. USSR-Sb., 64:2 (1989), 505–526
Citation in format AMSBIB
\paper On moment estimates for quasiderivative of solutions of stochastic equations with respect to the initial data, and their applications
\jour Mat. Sb. (N.S.)
\jour Math. USSR-Sb.
Citing articles on Google Scholar:
Related articles on Google Scholar:
This publication is cited in the following articles:
N. V. Krylov, “On control of diffusion processes on a surface in Euclidean space”, Math. USSR-Sb., 65:1 (1990), 185–203
N. V. Krylov, “Smoothness of the value function for a controlled diffusion process in a domain”, Math. USSR-Izv., 34:1 (1990), 65–95
N. V. Krylov, “On the first quasiderivatives of solutions of Ito stochastic equations”, Russian Acad. Sci. Izv. Math., 40:2 (1993), 377–403
Zhou W., “The Quasiderivative Method for Derivative Estimates of Solutions to Degenerate Elliptic Equations”, Stoch. Process. Their Appl., 123:8 (2013), 3064–3099
|Number of views:|