Abstract
In this paper we shall characterize the large deviation principles (abbreviated to LDP) of Donsker-Varadhan of a Markov process both for the weak convergence topology and for the τ-topology, by means of a hyper-exponential recurrence property. A Lyapunov criterion for this type of recurrence property is presented. These results are applied to countable Markov chains, unidimensional diffusions, elliptic or hypoelliptic diffusions on Rienmannian manifolds. Several counter-examples are equally presented.
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Received July 20, 1998, Accepted March 25, 1999
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Wu, L. Some Notes on Large Deviations of Markov Processes. Acta Mathematica Sinica, English Series 16, 369–394 (2000). https://doi.org/10.1007/PL00011549
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DOI: https://doi.org/10.1007/PL00011549