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The time variation of the rank $k$ of words for six Indo-European languagesis obtained using data from Google Books. For low ranks the distinct languagesbehave differently, maybe due to syntaxis rules, whereas for $k>50$ the law oflarge numbers predominates. The dynamics of $k$ is described stochasticallythrough a master equation governing the time evolution of its probabilitydensity, which is approximated by a Fokker-Planck equation that is solvedanalytically. The difference between the data and the asymptotic solution isidentified with the transient solution, and good agreement is obtained.

Rank-frequency distribution of natural languages: a difference of probabilities approach