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1 results

  • Stochastic calculus over symmetric Markov processes with time reversal

  • K. Kuwae
  • Journal:
    Nagoya Mathematical Journal / Volume 220 / December 2015
    Published online by Cambridge University Press:
    11 January 2016, pp. 91-148
    Print publication:
    December 2015
    • Article
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  • We develop stochastic calculus for symmetric Markov processes in terms of time reversal operators. For this, we introduce the notion of the progressively additive functional in the strong sense with time-reversible defining sets. Most additive functionals can be regarded as such functionals. We obtain a refined formula between stochastic integrals by martingale additive functionals and those by Nakao's divergence-like continuous additive functionals of zero energy. As an application, we give a stochastic characterization of harmonic functions on a domain with respect to the infinitesimal generator of semigroup on L2-space obtained by lower-order perturbations.