A Representation of the Relative Entropy with Respect to a Diffusion Process in Terms of Its Infinitesimal Generator
| Autor: | James MacLaurin, Olivier Faugeras |
|---|---|
| Přispěvatelé: | Mathematical and Computational Neuroscience (NEUROMATHCOMP), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA) |
| Jazyk: | angličtina |
| Rok vydání: | 2014 |
| Předmět: |
Kullback–Leibler divergence
General Physics and Astronomy lcsh:Astrophysics 01 natural sciences Kullback-Leibler 010104 statistics & probability lcsh:QB460-466 Statistical inference Infinitesimal generator 0101 mathematics lcsh:Science Mathematics Weak solution [SCCO.NEUR]Cognitive science/Neuroscience 010102 general mathematics Mathematical analysis relative entropy diffusion Empirical measure lcsh:QC1-999 Exponential function [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] martingale formulation Rate of convergence Kullback–Leibler lcsh:Q Martingale (probability theory) lcsh:Physics |
| Zdroj: | Entropy, Vol 16, Iss 12, Pp 6705-6721 (2014) Entropy Entropy, MDPI, 2014, 16, pp.17. ⟨10.3390/e16126705⟩ Volume 16 Issue 12 Pages 6705-6721 Entropy, 2014, 16, pp.17. ⟨10.3390/e16126705⟩ |
| ISSN: | 1099-4300 |
| Popis: | In this paper we derive an integral (with respect to time) representation of the relative entropy (or Kullback–Leibler Divergence) R(μ||P), where μ and P are measures on C([0,T] Rd). The underlying measure P is a weak solution to a martingale problem with continuous coefficients. Our representation is in the form of an integral with respect to its infinitesimal generator. This representation is of use in statistical inference (particularly involving medical imaging). Since R(μ||P) governs the exponential rate of convergence of the empirical measure (according to Sanov’s theorem), this representation is also of use in the numerical and analytical investigation of finite-size effects in systems of interacting diffusions. |
| Databáze: | OpenAIRE |
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