For a symmetric stable process we consider a transform of its transition semigroup by a non-local Feynman-Kac functional. We prove that if the Feynman-Kac functional belongs to a certain class, then the spectral bound of the transformed semigroup on L p (R d ) is independent of p .2000 Mathematics Subject Classification: 60J45, 60J40, 35J10.
Large deviation principles of occupation distribution for generalized Feynman-Kac functionals are presented in the framework of symmetric Markov processes having doubly Feller or strong Feller property. As a consequence, we obtain the L p -independence of spectral radius of our generalized Feynman-Kac functionals. We also prove Fukushima's decomposition in the strict sense for functions locally in the domain of Dirichlet form having energy measure of Dynkin class without assuming no inside killing.
We consider Lévy directed polymers in the Poisson random environment. We give conditions for strong or weak disorder in terms of the Lévy exponent of symmetric Lévy process.
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