On the specific relative entropy between martingale diffusions on the line
Abstract
The specific relative entropy, introduced by N. Gantert, allows to quantify the discrepancy between the laws of potentially mutually singular measures. It appears naturally as the large deviations rate function in a randomized version of Donsker's invariance principle, as well as in a novel transport-information inequality recently derived by H. Foellmer. A conjecture, put forward by the aforementioned authors, concerns a closed form expression for the specific relative entropy between continuous martingale laws in terms of their quadratic variations. We provide a first partial result in this direction, by establishing this conjecture in the case of well-behaved martingale diffusions on the line.
Cite
@article{arxiv.2207.03312,
title = {On the specific relative entropy between martingale diffusions on the line},
author = {Julio Backhoff-Veraguas and Clara Unterberger},
journal= {arXiv preprint arXiv:2207.03312},
year = {2023}
}
Comments
Proposition 1 (on a.s. convergence) has been added, and the bibliographical references extended