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

Masayoshi Takeda

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)

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 Lp-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 Lp-independence holds, and if one of the boundaries is natural, the Lp-independence holds if and only if the L2-spectral bound is non-positive.

Original languageEnglish
Pages (from-to)1097-1129
Number of pages33
JournalJournal of Theoretical Probability
Volume24
Issue number4
DOIs
Publication statusPublished - 2011 Dec

Keywords

  • Dirichlet form
  • Feynman-Kac semigroup
  • Large deviation
  • Spectral bound

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Statistics, Probability and Uncertainty

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