Abstract: In this talk, we discuss a portmanteau theorem establishing the equivalence between information projections on a Banach space, constrained Kullback-Leibler weighted control, finding the mode of a measure through Onsager-Machlup formalism and in the classical Wiener space case, an Euler-Lagrange equation. As one example of an application of our theorem, we discuss a Feynman-Kac type formula, showing that the solution to a second order linear ODE (or system of ODEs) is the mode of a particular diffusion. Our portmanteau theorem along with our Feynman-Kac result provides numerics and insight for solving these ODEs. Joint work with William Haskell and Harsha Honnappa.
