Mots-clés : Carathéodory function
@article{TVP_2017_62_2_a8,
author = {A. Kurushima and A. Piunovskiy and Y. Zhang},
title = {Nowak's theorem on probability measures induced by strategies revisited},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {405--414},
year = {2017},
volume = {62},
number = {2},
language = {en},
url = {http://geodesic.mathdoc.fr/item/TVP_2017_62_2_a8/}
}
TY - JOUR AU - A. Kurushima AU - A. Piunovskiy AU - Y. Zhang TI - Nowak's theorem on probability measures induced by strategies revisited JO - Teoriâ veroâtnostej i ee primeneniâ PY - 2017 SP - 405 EP - 414 VL - 62 IS - 2 UR - http://geodesic.mathdoc.fr/item/TVP_2017_62_2_a8/ LA - en ID - TVP_2017_62_2_a8 ER -
A. Kurushima; A. Piunovskiy; Y. Zhang. Nowak's theorem on probability measures induced by strategies revisited. Teoriâ veroâtnostej i ee primeneniâ, Tome 62 (2017) no. 2, pp. 405-414. http://geodesic.mathdoc.fr/item/TVP_2017_62_2_a8/
[1] C. D. Aliprantis, K. C. Border, Infinite dimensional analysis. A hitchhiker's guide, 3rd. ed., Springer, Berlin, 2006, xxii+703 pp. | MR | Zbl
[2] D. P. Bertsekas, S. E. Shreve, Stochastic optimal control. The discrete time case, Math. Sci. Eng., 139, Academic Press, Inc., New York–London, 1978, xiii+323 pp. | MR | MR | Zbl | Zbl
[3] N. Dunford, J. T. Schwartz, Linear operators, v. I, Pure Appl. Math., 7, General theory, Interscience Publishers, Inc., New York; Interscience Publishers, Ltd., London, 1958, xiv+858 pp. | MR | MR | Zbl
[4] M. Gemignani, Elementary topology, Corr. reprint of the 2nd ed., Dover Publications, Inc., New York, 1990, xii+270 pp. | MR
[5] O. Hernández-Lerma, J. B. Lasserre, Discrete-time {M}arkov control processes. Basic optimality criteria, Appl. Math. (N. Y.), 30, Springer-Verlag, New York, 1996, xiv+216 pp. | DOI | MR | Zbl
[6] C. J. Himmelberg, T. Parthasarathy, F. S. Van Vleck, “Optimal plans for dynamic programming problems”, Math. Oper. Res., 1:4 (1976), 390–394 | DOI | MR | Zbl
[7] E. Kubińska, “Approximation of Carathéodory functions and multifunctions”, Real Anal. Exchange, 30:1 (2004/2005), 351–359 | MR | Zbl
[8] A. S. Nowak, “On the weak topology on a space of probability measures induced by policies”, Bull. Polish Acad. Sci. Math., 36:3-4 (1989), 181–186 | MR | Zbl
[9] A. B. Piunovskiy, Optimal control of random sequences in problems with constraints, Math. Appl., 410, Kluwer Acad. Publ., Dordrecht, 1997, xii+345 pp. | DOI | MR | MR | Zbl
[10] M. Schäl, “On dynamic programming: compactness of the space of policies”, Stochastic Processes Appl., 3:4 (1975), 345–364 | DOI | MR | Zbl
[11] A. A. Yushkevich, “The compactness of a policy space in dynamic programming via an extension theorem for Carathéodory functions”, Math. Oper. Res., 22:2 (1997), 458–467 | DOI | MR | Zbl