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The Feynman–Kac Formula and Excursion Theory

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Part of the Lecture Notes in Mathematics book series (LNM,volume 2088)

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.

Keywords

  • Excursion Theory
  • Independent Exponential Time
  • Inverse Local Time
  • Wiener Measure
  • Brownian Motion

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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  4. M. Jeanblanc, J. Pitman, M. Yor, The Feynman–Kac formula and decomposition of Brownian paths. Sociedade Brasiliera de Matemática Applicada e Computacional. Matemática Aplicada e Computacional. Comput. Appl. Math. 16(1), 27–52 (1997)

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© 2013 Springer International Publishing Switzerland

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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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