Affiliations: [a] Departamento de Estadística y Cálculo, Universidad Autónoma Agraria Antonio Narro, Saltillo, COAH 25315, México. E-mail: rcavazos@uaaan.mx | [b] Centro de Investigación en Matemáticas, Guanajuato, GTO 36000, México. E-mail: dher@cimat.mx
Correspondence:
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Corresponding author: Daniel Hernández-Hernández, Centro de Investigación en Matemáticas, Apartado Postal 402, Guanajuato, GTO 36000, México. E-mail: dher@cimat.mx.
Abstract: This work concerns Markov chains evolving on a denumerable sate space, which is endowed with a non-negative reward function with finite support. In this context, the problem of determining the Varadhan function, given by the exponential growth rate of the aggregated rewards, is studied. The main results in this direction are expressed in terms of the idea of a system of local Poisson equations, and can be summarized as follows: (i) the Varadhan function is determined by one of such systems, and (ii) if a finite set is accessible form any state, then a system of local Poisson equations exits.
Keywords: discounted approximation, fixed points, stopping time, accessibility to a finite set, weak Doeblin condition, risk-sensitive average reward
