Geodesic
Estimates for perturbations of discounted Markov chains on general spaces
Raúl Montes-de-Oca1 ; Alexander Sakhanenko2 ; Francisco Salem-Silva3
1Departamento de Matemáticas Universidad Autónoma Metropolitana–Iztapalapa Av. San Rafael Atlixco 186, Col. Vicentina México D.F. 09340, Mexico
2Facultad de Ciencias Físico Matemáticas Benemérita Universidad Autónoma de Puebla Av. San Claudio y Río Verde Col. San Manuel, Ciudad Universitaria Puebla Pue. 72570, Mexico
3Facultad de Ciencias Físico Matemáticas Benemérita Universidad Autónoma de Puebla Av. San Claudio y Río Verde Col. San Manuel Ciudad Universitaria Puebla Pue. 72570, Mexico
Applicationes Mathematicae, Tome 30 (2003) no. 1, pp. 39-53
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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.
DOI : 10.4064/am30-1-3
Keywords: analyse markov chain perturbations transition probability one step cost function possibly unbounded defined under certain conditions lyapunov harris type obtain estimates effects perturbations via index perturbations defined difference total expected discounted costs between original markov chain perturbed provide example which illustrates analysis

Raúl Montes-de-Oca  1   ; Alexander Sakhanenko  2   ; Francisco Salem-Silva  3

1 Departamento de Matemáticas Universidad Autónoma Metropolitana–Iztapalapa Av. San Rafael Atlixco 186, Col. Vicentina México D.F. 09340, Mexico
2 Facultad de Ciencias Físico Matemáticas Benemérita Universidad Autónoma de Puebla Av. San Claudio y Río Verde Col. San Manuel, Ciudad Universitaria Puebla Pue. 72570, Mexico
3 Facultad de Ciencias Físico Matemáticas Benemérita Universidad Autónoma de Puebla Av. San Claudio y Río Verde Col. San Manuel Ciudad Universitaria Puebla Pue. 72570, Mexico 
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Raúl Montes-de-Oca; Alexander Sakhanenko; Francisco Salem-Silva. Estimates for perturbations of
 discounted Markov chains on general spaces. Applicationes Mathematicae, Tome 30 (2003) no. 1, pp. 39-53. doi: 10.4064/am30-1-3

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