On approximation of value functions for controlled discontinuous random processes

Abstract

We consider the problem of approximation of value functions for con- trolled possibly degenerated diffusion processes with jumps by using piece-wise con- stant control policies. A rate of convergence for the corresponding value functions is established provided that the coefficients of controlled processes are sufficiently smooth. The paper extends the results of N.V. Krylov to a more general class of controlled processes.