Research Article

A Stochastic Diffusion Process for the Dirichlet Distribution

Table 1

Initial and final states of the Monte Carlo simulation starting from a triple delta. The coefficients, , , , , , , of the system of SDEs (18)–(20) determine the distribution to which the system converges. The Dirichlet parameters, implied by the SDE coefficients via (15)–(17), are in brackets. The corresponding statistics are determined by the well-known formulae of Dirichlet distributions [2].

Initial state:
triple delta,
see Figure 1
SDE coefficients and the statistics of
their implied Dirichlet distribution in
the statistically stationary state