An Integral Representation of the Relative Entropy

被引：5
|
作者：
Hirata, Miku [2 ]
Nemoto, Aya [2 ]
Yoshida, Hiroaki [1 ]
机构：
[1] Ochanomizu Univ, Dept Informat Sci, Bunkyo Ku, Tokyo 1128610, Japan
[2] Ochanomizu Univ, Dept Math, Bunkyo Ku, Tokyo 1128610, Japan
来源：
ENTROPY | 2012年 / 14卷 / 08期
关键词：
relative entropy; relative Fisher information; de Bruijn identity; logarithmic Sobolev inequality; Stam inequality; LOGARITHMIC SOBOLEV INEQUALITIES; CENTRAL-LIMIT-THEOREM; FISHER INFORMATION; POWER;
D O I：
10.3390/e14081469
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
Recently the identity of de Bruijn type between the relative entropy and the relative Fisher information with the reference moving has been unveiled by Verdu via MMSE in estimation theory. In this paper, we shall give another proof of this identity in more direct way that the derivative is calculated by applying integrations by part with the heat equation. We shall also derive an integral representation of the relative entropy, as one of the applications of which the logarithmic Sobolev inequality for centered Gaussian measures will be given.
引用
收藏
页码：1469 / 1477
页数：9
相关论文
共 50 条
  • [21] Relative entropy and catalytic relative majorization
    Rethinasamy, Soorya
    Wilde, Mark M.
    PHYSICAL REVIEW RESEARCH, 2020, 2 (03):
  • [22] Relative Entropy and Relative Entropy of Entanglement for Infinite-Dimensional Systems
    Zhoubo Duan
    Lifang Niu
    Yangyang Wang
    Liang Liu
    International Journal of Theoretical Physics, 2017, 56 : 1929 - 1936
  • [23] Relative Entropy and Relative Entropy of Entanglement for Infinite-Dimensional Systems
    Duan, Zhoubo
    Niu, Lifang
    Wang, Yangyang
    Liu, Liang
    INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS, 2017, 56 (06) : 1929 - 1936
  • [24] SUBJECT REPRESENTATION AND ENTROPY
    IYER, H
    INTERNATIONAL CLASSIFICATION, 1992, 19 (01): : 15 - 18
  • [25] INTEGRAL REPRESENTATION ALGEBRAS
    REINER, I
    TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1966, 124 (01) : 111 - &
  • [26] INTEGRAL-REPRESENTATION
    CHOQUET, G
    LECTURE NOTES IN MATHEMATICS, 1983, 1033 : 114 - 141
  • [27] Semimartingale integral representation
    Ahn, H
    ANNALS OF PROBABILITY, 1997, 25 (02): : 997 - 1010
  • [28] Relative entropy and holography
    David D. Blanco
    Horacio Casini
    Ling-Yan Hung
    Robert C. Myers
    Journal of High Energy Physics, 2013
  • [29] Polynomials with an integral representation
    Cilia, Raffaella
    Gutierrez, Joaquin M.
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2017, 455 (01) : 246 - 262
  • [30] Fuzzy integral representation
    Ralescu, DA
    Sugeno, M
    FUZZY SETS AND SYSTEMS, 1996, 84 (02) : 127 - 133
12345