Julio Backhoff-Veraguas, Clara Unterberger
Published 2022-07-07Version 1
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.
Donsker's invariance principle under the sub-linear expectation with an application to Chung's law of the iterated logarithm
Ordinal optimization - empirical large deviations rate estimators, and stochastic multi-armed bandits
Large deviations for interacting multiscale particle systems
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