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 Electronic Journal of Probability > Vol. 4 (1999) > Paper 2 open journal systems 


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

N. V. Krylov, University of Minnesota


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 $[kh^{2},(k+1)h^{2})$.


Full text: PDF

Pages: 1-19

Published on: January 26, 1999


Bibliography
  1. M. Bardi and I. Cappuzo-Dolcetta (1997), Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations, Birkh"auser, Boston.
  2. I.I. Gihman, Certain differential equations with random functions, Ukrainski Mat. Zh., 2, 4 (1950), 37-63 Math Review link and 3, 3 (1951), 317-339 (in Russian), Math Review link
  3. W. Fleming and M. Soner (1993), Controlled Markov processes and viscosity solutions, Springer. Math Review link
  4. N.V. Krylov (1977), Controlled diffusion processes, Nauka, Moscow, in Russian; English translation: Springer, 1980. Math Review link
  5. 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. Math Review link
  6. N.V. Krylov, Mean value theorems for stochastic integrals, submitted to the Annals of Probability.
  7. 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.
















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Electronic Journal of Probability. ISSN: 1083-6489