We provide a generalization of Ueno's inequality for n-step transition probabilities of Markov chains in a general state space. Our result is relevant to the study of adaptive control problems and approximation problems in the theory of discrete-time Markov decision processes and stochastic games.
@article{bwmeta1.element.bwnjournal-article-zmv25i3p295bwm, author = {Andrzej Nowak}, title = {A generalization of Ueno's inequality for n-step transition probabilities}, journal = {Applicationes Mathematicae}, volume = {25}, year = {1998}, pages = {295-299}, zbl = {0998.60068}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-zmv25i3p295bwm} }
Nowak, Andrzej. A generalization of Ueno's inequality for n-step transition probabilities. Applicationes Mathematicae, Tome 25 (1998) pp. 295-299. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-zmv25i3p295bwm/
[000] [1] R. B. Ash, Real Analysis and Probability, Academic Press, New York, 1972.
[001] [2] J. P. Georgin, Contrôle de chaînes de Markov sur des espaces arbitraires, Ann. Inst. H. Poincaré Sér. B 14 (1978), 255-277. | Zbl 0391.60066
[002] [3] O. Hernandez-Lerma, Adaptive Markov Control Processes, Springer, New York, 1989.
[003] [4] N. W. Kartashov, Criteria for uniform ergodicity and strong stability of Markov chains in general state space, Probab. Theory Math. Statist. 30 (1984), 65-81.
[004] [5] G. B. Di Masi and Ł. Stettner, Bayesian ergodic adaptive control of discrete time Markov processes, Stochastics and Stochastics Reports 54 (1995), 301-316. | Zbl 0855.93103
[005] [6] A. S. Nowak and E. Altman, ε-Nash equilibria in stochastic games with uncountable state space and unbounded cost, Technical Report, Institute of Mathematics, Wrocław University of Technology, 1998.
[006] [7] W. J. Runggaldier and Ł. Stettner, Approximations of Discrete Time Partially Observed Control Problems, Appl. Math. Monographs 6, C.N.R., Pisa, 1994.
[007] [8] Ł. Stettner, On nearly self-optimizing strategies for a discrete-time uniformly ergodic adaptive model, Appl. Math. Optim. 27 (1993), 161-177. | Zbl 0769.93084
[008] [9] T. Ueno, Some limit theorems for temporally discrete Markov processes, J. Fac. Sci. Univ. Tokyo 7 (1957), 449-462. | Zbl 0077.33201