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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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Real-valued Deterministic Processes

Real-valued Deterministic Processes

Chapter:
(p.90) Chapter Six Real-valued Deterministic Processes
Source:
An Introduction to Benford's Law
Author(s):

Arno Berger

Theodore P. Hill

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691163062.003.0006

In science, one-dimensional deterministic (i.e., non-random) systems provide the simplest models for processes that evolve over time. Mathematically, these models take the form of one-dimensional difference or differential equations. This chapter presents the basic theory of Benford's law for them. Specifically, it studies conditions under which these models conform to Benford's law by generating Benford sequences and functions, respectively. The first seven sections of the chapter focus on discrete-time systems (i.e., difference equations) because they are somewhat easier to work with explicitly. Once the Benford properties of discrete-time systems are understood, it is straightforward to establish the analogous properties for continuous-time systems (i.e., differential equations), which is done in the chapter's final section.

Keywords:   Benford's law, one-dimensional deterministic systems, polynomial growth, exponential growth, superexponential growth, Benford sequences, Benford functions, one-dimensional difference, differential equations

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