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Applied Mathematics and Optimization

, Volume 53, Issue 1, pp 101–119 | Cite as

A System of Poisson Equations for a Nonconstant Varadhan Functional on a Finite State Space

  • Rolando Cavazos-CadenaEmail author
  • Daniel Hernandez-HernandezEmail author
Article

Abstract

Given a discrete-time Markov chain with finite state space and a stationary transition matrix, a system of "local" Poisson equations characterizing the (exponential) Varadhan's functional J(·) is given. The main results, which are derived for an arbitrary transition structure so that J(·) may be nonconstant, are as follows: (i) Any solution to the local Poisson equations immediately renders Varadhan's functional, and (ii) a solution of the system always exist. The proof of this latter result is constructive and suggests a method to solve the local Poisson equations.

Local Poisson equations Exponential grow rate Closed and communicating sets Risk-sensitive long-run average cost 

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Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Departamento de Estadistica y Calculo, Universidad Autonoma Agraria Antonio Narro, Buenavista, Saltillo, COAH 25315Mexico
  2. 2.Centro de Investigacion en Matematicas, Apartado Postal 402, Guanajuato,GTO 36000Mexico

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