Abstract
We provide a proof of the Feynman–Kac formula for Brownian motion, using excursion theory up to an independent exponential time θ. Call g(θ) the last zero before θ. The independence of the pre-g(θ) process and the post-g(θ) process and the representation of their laws in terms of the integrals of Wiener measure up to inverse local time, or first hitting times allow to recover a formulation of the Feynman–Kac formula via excursion theory.
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References
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Yen, JY., Yor, M. (2013). The Feynman–Kac Formula and Excursion Theory. In: Local Times and Excursion Theory for Brownian Motion. Lecture Notes in Mathematics, vol 2088. Springer, Cham. https://doi.org/10.1007/978-3-319-01270-4_10
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DOI: https://doi.org/10.1007/978-3-319-01270-4_10
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