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}
}
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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