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Log-growth distributions of US city sizes and non-Lévy processes

Ramos, Arturo (2015): Log-growth distributions of US city sizes and non-Lévy processes.

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Abstract

We study whether the hypothesis that the log-population of US cities follows a Lévy process can be rejected or not. The result seems to be rejection.

As a consequence, the cited process seems not to be described by a standard Brownian motion with drift (with a Yule process), thus explaining in another way the rejection of the lognormal and double Pareto lognormal distributions for US city size in recent studies. The datasets employed are that of US incorporated places on the period 1890-2000.

However, we recall a way of obtaining a family of stochastic Itô differential equations whose sample paths are associated to the time-dependent probability density functions for city size that in principle could be observed empirically

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