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.
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Manuscript received: August 2003 / Final version received: January 2004
This work was supported by the PSF Organization under Grant No. 010/300/01-5, and Conacyt Grant No. 37643–E.
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Cavazos–Cadena, R., Hernández–Hernández, D. A characterization of exponential functionals in finite Markov chains. Math Meth Oper Res 60, 399–414 (2004). https://doi.org/10.1007/s001860400373
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DOI: https://doi.org/10.1007/s001860400373