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

A System of Poisson Equations for a Nonconstant Varadhan Functional on a Finite State Space 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

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

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Copyright © 2006 by Springer
Mathematics; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization; Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Methods
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