## Electronic Journal of Probability

### Approximating Value Functions for Controlled Degenerate Diffusion Processes by Using Piece-Wise Constant Policies

N. Krylov

#### Abstract

It is shown that value functions for controlled degenerate diffusion processes can be approximated with error of order $h^{1/3}$ by using policies which are constant on intervals $[kh^{2},(k+1)h^{2})$.

#### Article information

Source
Electron. J. Probab. Volume 4 (1999), paper no. 2, 19 pp.

Dates
Accepted: 26 January 1999
First available in Project Euclid: 4 March 2016

http://projecteuclid.org/euclid.ejp/1457125511

Digital Object Identifier
doi:10.1214/EJP.v4-39

Mathematical Reviews number (MathSciNet)
MR1668597

Zentralblatt MATH identifier
1044.93546

Subjects
Primary: 93E20: Optimal stochastic control
Secondary: 35K55: Nonlinear parabolic equations

Rights

#### Citation

Krylov, N. Approximating Value Functions for Controlled Degenerate Diffusion Processes by Using Piece-Wise Constant Policies. Electron. J. Probab. 4 (1999), paper no. 2, 19 pp. doi:10.1214/EJP.v4-39. http://projecteuclid.org/euclid.ejp/1457125511.

#### References

• M. Bardi and I. Cappuzo-Dolcetta (1997), Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations, Birkh"auser, Boston.
• I.I. Gihman, Certain differential equations with random functions, Ukrainski Mat. Zh., 2, 4 (1950), 37-63
• W. Fleming and M. Soner (1993), Controlled Markov processes and viscosity solutions, Springer.
• N.V. Krylov (1977), Controlled diffusion processes, Nauka, Moscow, in Russian; English translation: Springer, 1980.
• N.V. Krylov (1997), On the rate of convergence of finite–difference approximations for Bellman's equations, Algebra i Analiz, St. Petersburg Math. J., 9, 3, 245-256.
• N.V. Krylov, Mean value theorems for stochastic integrals, submitted to the Annals of Probability.
• N.V. Krylov, On the rate of convergence of finite–difference approximations for Bellman's equations with variable coefficients, submitted to Probability Theory and Related Fields.