TY - JOUR
T1 - Entropy flow and de bruijn's identity for a class of stochastic differential equations driven by fractional brownian motion
AU - Choi, Michael C.H.
AU - Lee, Chihoon
AU - Song, Jian
N1 - Publisher Copyright:
Copyright © Cambridge University Press 2019.
PY - 2021/7
Y1 - 2021/7
N2 - Motivated by the classical De Bruijn's identity for the additive Gaussian noise channel, in this paper we consider a generalized setting where the channel is modelled via stochastic differential equations driven by fractional Brownian motion with Hurst parameter H â (0, 1). We derive generalized De Bruijn's identity for Shannon entropy and Kullback-Leibler divergence by means of Itô's formula, and present two applications. In the first application we demonstrate its equivalence with Stein's identity for Gaussian distributions, while in the second application, we show that for H â (0, 1/2], the entropy power is concave in time while for H â (1/2, 1) it is convex in time when the initial distribution is Gaussian. Compared with the classical case of H = 1/2, the time parameter plays an interesting and significant role in the analysis of these quantities.
AB - Motivated by the classical De Bruijn's identity for the additive Gaussian noise channel, in this paper we consider a generalized setting where the channel is modelled via stochastic differential equations driven by fractional Brownian motion with Hurst parameter H â (0, 1). We derive generalized De Bruijn's identity for Shannon entropy and Kullback-Leibler divergence by means of Itô's formula, and present two applications. In the first application we demonstrate its equivalence with Stein's identity for Gaussian distributions, while in the second application, we show that for H â (0, 1/2], the entropy power is concave in time while for H â (1/2, 1) it is convex in time when the initial distribution is Gaussian. Compared with the classical case of H = 1/2, the time parameter plays an interesting and significant role in the analysis of these quantities.
KW - de bruijn's identity
KW - entropy power
KW - fokker-planck equation
KW - fractional brownian motion
UR - http://www.scopus.com/inward/record.url?scp=85076996803&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85076996803&partnerID=8YFLogxK
U2 - 10.1017/S0269964819000421
DO - 10.1017/S0269964819000421
M3 - Article
AN - SCOPUS:85076996803
SN - 0269-9648
VL - 35
SP - 369
EP - 380
JO - Probability in the Engineering and Informational Sciences
JF - Probability in the Engineering and Informational Sciences
IS - 3
ER -