We consider the problem of approximation of value functions for controlled possibly degenerated diffusion processes with jumps by using piece-wise constant 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.
Danilenko, S., & Pragarauskas, H. (2011). On approximation of value functions for controlled discontinuous random processes. Mathematical Modelling and Analysis, 16(2), 260-272. https://doi.org/10.3846/13926292.2011.580015
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