Geodesic
Approximation and estimation in Markov control processes under a discounted criterion
Kybernetika, Tome 40 (2004) no. 6, p. [681].

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We consider a class of discrete-time Markov control processes with Borel state and action spaces, and $\Re ^{k}$-valued i.i.d. disturbances with unknown density $\rho .$ Supposing possibly unbounded costs, we combine suitable density estimation methods of $\rho $ with approximation procedures of the optimal cost function, to show the existence of a sequence $\lbrace \hat{f}_{t}\rbrace $ of minimizers converging to an optimal stationary policy $f_{\infty }.$
Classification : 90B05, 90B30, 90C40, 93E10
Keywords: Markov control processes; density estimation; discounted cost criterion 
@article{KYB_2004__40_6_a2,
     author = {Minj\'arez-Sosa, J. Adolfo},
     title = {Approximation and estimation in {Markov} control processes under a discounted criterion},
     journal = {Kybernetika},
     pages = {[681]},
     publisher = {mathdoc},
     volume = {40},
     number = {6},
     year = {2004},
     mrnumber = {2120390},
     zbl = {1249.93163},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2004__40_6_a2/}
}
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Minjárez-Sosa, J. Adolfo. Approximation and estimation in Markov control processes under a discounted criterion. Kybernetika, Tome 40 (2004) no. 6, p. [681]. http://geodesic.mathdoc.fr/item/KYB_2004__40_6_a2/