A characterization of exponential functionals in finite Markov chains

Rolando Cavazos–Cadena () and Daniel Hernández–Hernández ()

Mathematical Methods of Operations Research, 2004, vol. 60, issue 3, 399-414

Abstract: This work considers Markov chains with finite state space. It is supposed that the process has a single recurrent class, but the set of transient states is not necessarily empty. In this context, a Varadhan’s function, giving the exponential grow rate of an aggregated cost function, is studied. The main result establishes that this functional is the optimal value of a minimization problem on the Euclidean space whose dimension equals the number of states. Copyright Springer-Verlag 2004

Keywords: Exponential grow rate; Single recurrent class; Transient states; Risk–sensitive average cost; 60J05; 60F10 (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1007/s001860400373

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