  We present a mathematical formulation of a theory of language change. The
theory is evolutionary in nature and has close analogies with theories of
population genetics. The mathematical structure we construct similarly has
correspondences with the Fisher-Wright model of population genetics, but there
are significant differences. The continuous time formulation of the model is
expressed in terms of a Fokker-Planck equation. This equation is exactly
soluble in the case of a single speaker and can be investigated analytically in
the case of multiple speakers who communicate equally with all other speakers
and give their utterances equal weight. Whilst the stationary properties of
this system have much in common with the single-speaker case, time-dependent
properties are richer. In the particular case where linguistic forms can become
extinct, we find that the presence of many speakers causes a two-stage
relaxation, the first being a common marginal distribution that persists for a
long time as a consequence of ultimate extinction being due to rare
fluctuations.
