A de Bruijn identity for discrete random variables

Oliver Johnson, Saikat Guha

Research output: Contribution to journalArticlepeer-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 languageEnglish (US)
JournalUnknown Journal
StatePublished - Jan 23 2017
Externally publishedYes

ASJC Scopus subject areas

  • General

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