A Stochastic Model of Language Change Through Social Structure and Prediction-Driven Instability

We develop a new stochastic model of language learning and change that incorporates variable speech and age structure. Children detect correlations between age and speech, predict how the language is changing, and speak according to that prediction. Although the population tends to be dominated by one idealized grammar or another, the learning process amplifies chance correlation between age and speech, generating prediction-driven instability and spontaneous language change. The model is formulated as a Markov chain, and a stochastic differential equation. It exhibits the abrupt monotonic shifts among equilibria characteristic of language changes. Fundamental results are proved. 1. The paradox of language change Language has both discrete and continuous characteristics. On the discrete side, most sentences are clearly either grammatical or ungrammatical. An idealized grammar is a formalism that identifies correct utterances, and much of the research on how children acquire their native language focuses on how they might choose an idealized grammar from many innate possibilities on the basis of example sentences from