A Stochastic Diffusion Process for the Dirichlet Distribution
Figure 1
Time evolution of the joint probability, , extracted from the numerical solution of (18)–(20). The initial condition is a triple-delta distribution, with unequal peaks at the three corners of the sample space. At the end of the simulation, , the solid lines are those of the distribution extracted from the numerical ensemble, and the dashed lines are those of a Dirichlet distribution to which the solution converges in the statistically stationary state, implied by the constant SDE coefficients, sampled at the same heights.
