Zhang, J. Jeffreys Divergence and Generalized Fisher Information Measures on Fokker–Planck Space–Time Random Field. Entropy2023, 25, 1445.
Zhang, J. Jeffreys Divergence and Generalized Fisher Information Measures on Fokker–Planck Space–Time Random Field. Entropy 2023, 25, 1445.
Zhang, J. Jeffreys Divergence and Generalized Fisher Information Measures on Fokker–Planck Space–Time Random Field. Entropy2023, 25, 1445.
Zhang, J. Jeffreys Divergence and Generalized Fisher Information Measures on Fokker–Planck Space–Time Random Field. Entropy 2023, 25, 1445.
Abstract
In this paper, we derive Jeffreys divergence, generalized Fisher divergence and corresponding De Bruijn identities on space-time random field. First, we determine the relation between Fisher information on the space-time random field in one of the space-time points and the ratio of Jeffreys divergence on a space-time random field at distinct space-time positions to the square of coordinate difference. In addition, we also find identities between the partial derivative of the Jeffreys divergence and the generalized Fisher divergence with respect to space-time variables, i.e. the De Bruijn identities, between two space-time random fields obtained by different parameters under the same Fokker-Planck equations. At the end of this paper, we present three examples of the Fokker-Planck equations on space-time random fields, identify their density functions, and derive the Jeffreys divergence, generalized Fisher information, generalized Fisher divergence, and accompanying De Bruijn identities.
Keywords
Space-time random field; Fokker-Planck equations; Differential entropy; Jeffreys divergence; Fisher information; De Bruijn identities
Subject
Computer Science and Mathematics, Applied Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
