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

@article{Selk2021AFT, title={A Feynman-Kac Type Theorem for ODEs: Solutions of Second Order ODEs as Modes of Diffusions}, author={Zachary Selk and Harsha Honnappa}, journal={ArXiv}, year={2021}, volume={abs/2106.08525} }

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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Numerical evaluation of ODE solutions by Monte Carlo enumeration of Butcher series

- Computer Science, MathematicsArXiv
- 2022

The Monte Carlo scheme allows for the direct numerical evaluation of an ODE solution at any given time within a certain interval, without iteration through multiple time steps, and it does not require the truncation of Taylor series.

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