Estimates for perturbations of average Markov decision processes with a minimal state and upper bounded by stochastically ordered Markov chains

Raúl Montes-de-Oca; Francisco Salem-Silva

Displaying similar documents to “Estimates for perturbations of average Markov decision processes with a minimal state and upper bounded by stochastically ordered Markov chains”

Estimates for perturbations of general discounted Markov control chains

Raúl Montes-de-Oca, Alexander Sakhanenko, Francisco Salem-Silva (2003)

Applicationes Mathematicae

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We extend previous results of the same authors ([11]) on the effects of perturbation in the transition probability of a Markov cost chain for discounted Markov control processes. Supposing valid, for each stationary policy, conditions of Lyapunov and Harris type, we get upper bounds for the index of perturbations, defined as the difference of the total expected discounted costs for the original Markov control process and the perturbed one. We present examples that satisfy our conditions. ...

Estimates of stability of Markov control processes with unbounded costs

Evgueni I. Gordienko, Francisco Salem-Silva (2000)

Kybernetika

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For a discrete-time Markov control process with the transition probability $p$ , we compare the total discounted costs $V_{β}$ $(π_{β})$ and $V_{β} ({\tilde{π}}_{β})$ , when applying the optimal control policy $π_{β}$ and its approximation ${\tilde{π}}_{β}$ . The policy ${\tilde{π}}_{β}$ is optimal for an approximating process with the transition probability $\tilde{p}$ . A cost per stage for considered processes can be unbounded. Under certain ergodicity assumptions we establish the upper bound for the relative stability index $[V_{β} ({\tilde{π}}_{β}) - V_{β} (π_{β})] / V_{β} (π_{β})$ . This bound does not depend...

Estimates for perturbations of discounted Markov chains on general spaces

Raúl Montes-de-Oca, Alexander Sakhanenko, Francisco Salem-Silva (2003)

Applicationes Mathematicae

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We analyse a Markov chain and perturbations of the transition probability and the one-step cost function (possibly unbounded) defined on it. Under certain conditions, of Lyapunov and Harris type, we obtain new estimates of the effects of such perturbations via an index of perturbations, defined as the difference of the total expected discounted costs between the original Markov chain and the perturbed one. We provide an example which illustrates our analysis.

Invariant probabilities for Feller-Markov chains.

Hernández-Lerma, Onésimo, Lasserre, Jean B. (1995)

Journal of Applied Mathematics and Stochastic Analysis

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Bibliography on Markov chains with a general state space

Zbyněk Šidák (1976)

Aplikace matematiky

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A generalization of Ueno's inequality for n-step transition probabilities

Andrzej Nowak (1998)

Applicationes Mathematicae

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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.