Asymptotic Properties of Generalized Feynman–Kac Functionals

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Let (ℰ,ℱ) be a regular Dirichlet form on L2(X;m) and {Px}x ∈ X the Hunt process generated by (ℰ,ℱ). Let μ be a signed ‘smooth measure’ associated with (ℰ,ℱ) and Aμt the continuous additive functional corresponding to the measure μ. Under some conditions on (ℰ,ℱ) and μ, we shall prove that

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