Abstract
Abstract
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 ∈ (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 ∈ (0, 1/2], the entropy power is concave in time while for H ∈ (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.
Publisher
Cambridge University Press (CUP)
Subject
Industrial and Manufacturing Engineering,Management Science and Operations Research,Statistics, Probability and Uncertainty,Statistics and Probability
Cited by
1 articles.
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