Abstract
We establish a large deviation principle for the occupation distribution of a symmetric Markov process with Feynman–Kac functional. As an application, we show the L p-independence of the spectral bounds of a Feynman–Kac semigroup. In particular, we consider one-dimensional diffusion processes and show that if no boundaries are natural in Feller’s boundary classification, the L p-independence holds, and if one of the boundaries is natural, the L p-independence holds if and only if the L 2-spectral bound is non-positive.
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The author was supported in part by Grant-in-Aid for Scientific Research No. 18340033 (B), Japan Society for the Promotion of Science.
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Takeda, M. A Large Deviation Principle for Symmetric Markov Processes with Feynman–Kac Functional. J Theor Probab 24, 1097–1129 (2011). https://doi.org/10.1007/s10959-010-0324-5
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DOI: https://doi.org/10.1007/s10959-010-0324-5