This article is cited in 10 scientific papers (total in 10 papers)
On controlled diffusion processes with unbounded coefficients
N. V. Krylov
The paper is devoted to the general theory of controlled diffusion processes in a domain of a $d$-dimensional space in the absence of constraints on the growth of the coefficients at infinity. It turned out that the most suitable object of study is the payoff function in the optimal stopping problem for the controlled process. A theory analogous to the theory of controlled processes in the whole space, with growth constraints on the coefficients, is developed under natural assumptions.
Bibliography: 16 titles.
PDF file (2773 kB)
Mathematics of the USSR-Izvestiya, 1982, 19:1, 41–64
MSC: 60J60, 65G40, 93E20
N. V. Krylov, “On controlled diffusion processes with unbounded coefficients”, Izv. Akad. Nauk SSSR Ser. Mat., 45:4 (1981), 734–759; Math. USSR-Izv., 19:1 (1982), 41–64
Citation in format AMSBIB
\paper On~controlled diffusion processes with unbounded coefficients
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\jour Math. USSR-Izv.
Citing articles on Google Scholar:
Related articles on Google Scholar:
This publication is cited in the following articles:
N. V. Krylov, “On control of a diffusion process up to the time of first exit from a region”, Math. USSR-Izv., 19:2 (1982), 297–313
N. V. Krylov, “Boundedly nonhomogeneous elliptic and parabolic equations”, Math. USSR-Izv., 20:3 (1983), 459–492
N. V. Krylov, “On degenerate nonlinear elliptic equations. II”, Math. USSR-Sb., 49:1 (1984), 207–228
N. V. Krylov, “Boundedly nonhomogeneous elliptic and parabolic equations in a domain”, Math. USSR-Izv., 22:1 (1984), 67–97
N. V. Krylov, “On unconditional solvability of the Bellman equation with constant coefficients in convex domains”, Math. USSR-Sb., 63:2 (1989), 289–303
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
Joseph B. Keller, Hans F. Weinberger, “Boundary and initial boundary-value problems for separable backward–forward parabolic problems”, J Math Phys (N Y ), 38:8 (1997), 4343
O. Alvarez, “A quasilinear elliptic equation in ℝN”, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 126:05 (2011), 911
D. B. Rokhlin, “On the dynamic programming principle for controlled diffusion processes in a cylindrical region”, Sib. elektron. matem. izv., 10 (2013), 302–310
|Number of views:|