On Averaged Expected Cost Control for 1D Ergodic Diffusions with Switching
2023, v.29, Issue 2, 259-294
The ergodic Bellman's (HJB) equation is proved for a one-dimen\-sion\-al controlled diffusion with switching with variable diffusion and drift coefficients both depending on control; the intensities of transitions of the discrete component are constant. Its existence and uniqueness is established. Also, the convergence of the reward iteration improvement algorithm is established to the cost constant of the problem.
Keywords: controlled diffusion; switching; ergodicity; averaged control; Bellman's equation; reward improvement algorithm