Costa’s concavity inequality for dependent variables based on the multivariate Gaussian copula

IF 0.7 4区 数学 Q3 STATISTICS & PROBABILITY
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引用次数: 0

Abstract

An extension of Shannon’s entropy power inequality when one of the summands is Gaussian was provided by Costa in 1985, known as Costa’s concavity inequality. We consider the additive Gaussian noise channel with a more realistic assumption, i.e. the input and noise components are not independent and their dependence structure follows the well-known multivariate Gaussian copula. Two generalizations for the first- and second-order derivatives of the differential entropy of the output signal for dependent multivariate random variables are derived. It is shown that some previous results in the literature are particular versions of our results. Using these derivatives, concavity of the entropy power, under certain mild conditions, is proved. Finally, special one-dimensional versions of our general results are described which indeed reveal an extension of the one-dimensional case of Costa’s concavity inequality to the dependent case. An illustrative example is also presented.
基于多元高斯copula的因变量的Costa凹性不等式
1985年,Costa对其中一个被加数是高斯的Shannon熵权不等式进行了扩展,称为Costa凹性不等式。我们用一个更现实的假设来考虑加性高斯噪声信道,即输入和噪声分量不是独立的,它们的依赖结构遵循众所周知的多元高斯copula。导出了相依多元随机变量输出信号微分熵的一阶和二阶导数的两个推广。研究表明,文献中先前的一些结果是我们结果的特定版本。利用这些导数,在一定的温和条件下,证明了熵权的凹性。最后,描述了我们的一般结果的特殊一维版本,这确实揭示了Costa凹性不等式的一维情况对相依情况的扩展。并举例说明。
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来源期刊
Journal of Applied Probability
Journal of Applied Probability 数学-统计学与概率论
CiteScore
1.50
自引率
10.00%
发文量
92
审稿时长
6-12 weeks
期刊介绍: Journal of Applied Probability is the oldest journal devoted to the publication of research in the field of applied probability. It is an international journal published by the Applied Probability Trust, and it serves as a companion publication to the Advances in Applied Probability. Its wide audience includes leading researchers across the entire spectrum of applied probability, including biosciences applications, operations research, telecommunications, computer science, engineering, epidemiology, financial mathematics, the physical and social sciences, and any field where stochastic modeling is used. A submission to Applied Probability represents a submission that may, at the Editor-in-Chief’s discretion, appear in either the Journal of Applied Probability or the Advances in Applied Probability. Typically, shorter papers appear in the Journal, with longer contributions appearing in the Advances.
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