A de Bruijn identity for discrete random variables

Oliver Johnson; Saikat Guha

A de Bruijn identity for discrete random variables

Research output: Contribution to journal › Article › peer-review

Abstract

We discuss properties of the “beamsplitter addition” operation, which provides a non-standard scaled convolution of random variables supported on the non-negative integers. We give a simple expression for the action of beamsplitter addition using generating functions. We use this to give a self-contained and purely classical proof of a heat equation and de Bruijn identity, satisfied when one of the variables is geometric.

Original language	English (US)
Journal	Unknown Journal
State	Published - Jan 23 2017
Externally published	Yes

ASJC Scopus subject areas

General

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abstract = "We discuss properties of the “beamsplitter addition” operation, which provides a non-standard scaled convolution of random variables supported on the non-negative integers. We give a simple expression for the action of beamsplitter addition using generating functions. We use this to give a self-contained and purely classical proof of a heat equation and de Bruijn identity, satisfied when one of the variables is geometric.",

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