A Dynamic Model for the Two-Parameter Dirichlet Process

Let α = 1/2, θ > − 1/2, and ν0 be a probability measure on a type space S. In this paper, we investigate the stochastic dynamic model for the two-parameter Dirichlet process πα,θ,ν0$${\Pi }_{\alpha ,\theta ,\nu _{0}}$$. If S = ℕ, we show that the bilinear form 𝓔(F,G)=12∫𝓟1(ℕ)〈∇F(μ),∇G(μ)〉μπα,θ,ν0(dμ),F,G∈𝓕,𝓕={F(μ)=f(μ(1),…,μ(d)):f∈C∞(ℝd),d≥1}$$\begin{array}{@{}rcl@{}} \left\{ \begin{array}{l} …