Stein恒等式与de Bruijn恒等式的等价性
On the equivalence between Stein and de Bruijn identities
摘要：
本文主要证明Stein恒等式与de Bruijn恒等式之间的等价性。在一定条件下，证明了Stein恒等式与de Bruijn恒等式等价.此外，给出了de Bruijn恒等式的一些推广.对于任意但固定的输入和噪声分布，微分熵的一阶导数和后验均值之间存在关系。此外，微分熵的二阶导数与任意输入和噪声分布的Fisher信息有关。几个应用程序，以支持本文中开发的结果的有用性。
英文摘要：
This paper focuses on proving the equivalence between Stein's identity and de Bruijn's identity. Given some conditions, we prove that Stein's identity is equivalent to de Bruijn's identity. In addition, some extensions of de Bruijn's identity are presented. For arbitrary but fixed input and noise distributions, there exist relations between the first derivative of the differential entropy and the posterior mean. Moreover, the second derivative of the differential entropy is related to the Fisher information for arbitrary input and noise distributions. Several applications are presented to support the usefulness of the developed results in this paper.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
