Abstract
We prove that the Cramér functional of a Markov process can be controlled by a function of an integral functional if the transition semigroup is uniformly integrable in L p. As an application of this result, a general large deviation upper bound is obtained. Then, the notation of F-Sobolev inequality is extended to general Markov processes by replacing the Dirichlet form with the Donsker–Varadhan entropy. As the other application, it is proved that the uniform integrability of a transition semigroup implies a F-Sobolev inequality.
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Gao, F., Wang, Q. Upper Bound Estimates of the Cramér Functionals for Markov Processes. Potential Analysis 19, 383–398 (2003). https://doi.org/10.1023/A:1024165205229
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DOI: https://doi.org/10.1023/A:1024165205229