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

Journal Article · Sun Jan 15 00:00:00 EST 2006 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S00245-005-0840-3· OSTI ID:21067426

Cavazos-Cadena, Rolando ^[1]; Hernandez-Hernandez, Daniel ^[2]

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

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.

• OSTI ID: 21067426
• Journal Information: Applied Mathematics and Optimization, Vol. 53, Issue 1; Other Information: DOI: 10.1007/s00245-005-0840-3; Copyright (c) 2006 Springer; www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
MARKOV PROCESS
MATHEMATICAL SOLUTIONS
MATHEMATICAL SPACE
MATRICES
POISSON EQUATION