# Hamilton-Jacobi Theory and Information Geometry

@inproceedings{Ciaglia2017HamiltonJacobiTA,
title={Hamilton-Jacobi Theory and Information Geometry},
author={Florio M. Ciaglia and Fabio Di Cosmo and Giuseppe Marmo},
booktitle={International Conference on Geometric Science of Information},
year={2017}
}
• Published in
International Conference on…
3 November 2017
• Mathematics
Recently, a method to dynamically define a divergence function D for a given statistical manifold $$(\mathcal {M}\,,g\,,T)$$ by means of the Hamilton-Jacobi theory associated with a suitable Lagrangian function $$\mathfrak {L}$$ on $$T\mathcal {M}$$ has been proposed. Here we will review this construction and lay the basis for an inverse problem where we assume the divergence function D to be known and we look for a Lagrangian function $$\mathfrak {L}$$ for which D is a complete solution of the…
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