A Large Deviation Principle for Symmetric Markov Processes with Feynman–Kac Functional

Masayoshi Takeda ()
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Masayoshi Takeda: Tohoku University

Journal of Theoretical Probability, 2011, vol. 24, issue 4, 1097-1129

Abstract: 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.

Keywords: Large deviation; Feynman–Kac semigroup; Spectral bound; Dirichlet form; 60J45; 60J40; 35J10 (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/s10959-010-0324-5

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