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Bivariate Revuz Measures and the Feynman-Kac Formula on Semi-Dirichlet Forms

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Abstract

In this paper we shall first establish the theory of bivariate Revuz correspondence of positive additive functionals under a semi-Dirichlet form which is associated with a right Markov process X satisfying the sector condition but without duality. We extend most of the classical results about the bivariate Revuz measures under the duality assumptions to the case of semi-Dirichlet forms. As the main results of this paper, we prove that for any exact multiplicative functional M of X, the subprocess X M of X killed by M also satisfies the sector condition and we then characterize the semi-Dirichlet form associated with X M by using the bivariate Revuz measure, which extends the classical Feynman-Kac formula.

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Authors and Affiliations

  1. School of Mathematical Sciences, Fudan University, Rm 1818, Guanghua East Tower, 220 Handan Road, Shanghai, 200433, China

    Liping Li & Jiangang Ying

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  1. Liping Li
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  2. Jiangang Ying
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Correspondence to Liping Li.

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Li, L., Ying, J. Bivariate Revuz Measures and the Feynman-Kac Formula on Semi-Dirichlet Forms. Potential Anal 42, 775–808 (2015). https://doi.org/10.1007/s11118-014-9457-y

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