Estimates for perturbations of discounted Markov chains on general spaces

Volume 30 / 2003

Raúl Montes-de-Oca, Alexander Sakhanenko, Francisco Salem-Silva Applicationes Mathematicae 30 (2003), 39-53 MSC: 60J10, 93D05, 93D09. DOI: 10.4064/am30-1-3

Abstract

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.

Authors

  • Raúl Montes-de-OcaDepartamento de Matemáticas
    Universidad Autónoma
    Metropolitana–Iztapalapa
    Av. San Rafael Atlixco 186, Col. Vicentina
    México D.F. 09340, Mexico
    e-mail
  • Alexander SakhanenkoFacultad de Ciencias Físico Matemáticas
    Benemérita Universidad
    Autónoma de Puebla
    Av. San Claudio y Río Verde
    Col. San Manuel, Ciudad Universitaria
    Puebla Pue. 72570, Mexico
  • Francisco Salem-SilvaFacultad de Ciencias Físico Matemáticas
    Benemérita Universidad Autónoma de Puebla
    Av. San Claudio y Río Verde
    Col. San Manuel Ciudad Universitaria
    Puebla Pue. 72570, Mexico
    e-mail

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