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An Introduction to Benford's Law$
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Arno Berger and Theodore P. Hill

Print publication date: 2015

Print ISBN-13: 9780691163062

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691163062.001.0001

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Multi-dimensional Linear Processes

Multi-dimensional Linear Processes

(p.135) Chapter Seven Multi-dimensional Linear Processes
An Introduction to Benford's Law

Arno Berger

Theodore P. Hill

Princeton University Press

Chapter 6 studied models based solely on the one-dimensional processes, however, for many applications, these models are often too simple and have to be replaced with or complemented by more sophisticated multi-dimensional models. This chapter studies Benford's law in the simplest deterministic multi-dimensional processes, namely, linear processes in discrete and continuous time. Despite their simplicity, these systems provide important models for many areas of science. Through far-reaching generalizations of results from earlier chapters, they will be shown to very often conform to Benford's law in that their dynamics is an abundant source of Benford sequences and functions. As in the previous chapter, the properties of continuous-time systems (i.e., differential equations) are analogous to those of discrete-time systems, and the chapter focuses on the latter in every but its last section.

Keywords:   Benford's law, multi-dimensional models, linear processes, Benford sequences, Benford functions, differential equations

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