Abstract
Let \((\tfrac{1}{2}D,H^1 (R^d ))\) be the Dirichlet integral and \((B_t ,P_z^W )\) the Brownian motion on R. Let μ be a finite positive measure in the Kato class and \(A_t^\mu \) the additive functional associated with μ. We prove that for a regular domain D of R d
where τ D is the exit time from D. As an application, we consider the integrability of Wiener functional exp (\(A_{\tau _D }^\mu \)).
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Takeda, M. Exponential Decay of Lifetimes and a Theorem of Kac on Total Occupation Times. Potential Analysis 11, 235–247 (1999). https://doi.org/10.1023/A:1008649623291
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DOI: https://doi.org/10.1023/A:1008649623291