• Corpus ID: 235446802

A Feynman-Kac Type Theorem for ODEs: Solutions of Second Order ODEs as Modes of Diffusions

  title={A Feynman-Kac Type Theorem for ODEs: Solutions of Second Order ODEs as Modes of Diffusions},
  author={Zachary Selk and Harsha Honnappa},
In this article, we prove a Feynman-Kac type result for a broad class of second order ordinary differential equations. The classical Feynman-Kac theorem says that the solution to a broad class of second order parabolic equations is the mean of a particular diffusion. In our situation, we show that the solution to a system of second order ordinary differential equations is the mode of a diffusion, defined through the Onsager-Machlup formalism. One potential utility of our result is to use Monte… 
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