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The two-parameter Poisson-Dirichlet distribution is the law of a sequence of decreasing nonnegative random variables with total sum one. It can be constructed from stable and Gamma subordinators with the two-parameters, $alpha$ and $theta$, corresponding to the stable component and Gamma component respectively. The moderate deviation principles are established for the two-parameter Poisson-Dirichlet distribution and the corresponding homozygosity when $theta$ approaches infinity, and the large deviation principle is established for the two-parameter Poisson-Dirichlet distribution when both $alpha$ and $theta$ approach zero.
The two parameter Poisson-Dirichlet distribution $PD(alpha,theta)$ is the distribution of an infinite dimensional random discrete probability. It is a generalization of Kingmans Poisson-Dirichlet distribution. The two parameter Dirichlet process $Pi_
The two-parameter Poisson--Dirichlet diffusion, introduced in 2009 by Petrov, extends the infinitely-many-neutral-alleles diffusion model, related to Kingmans one-parameter Poisson--Dirichlet distribution and to certain Fleming--Viot processes. The a
The two-parameter Poisson-Dirichlet diffusion is an infinite-dimensional diffusion on the ordered simplex with a two-parameter Poisson-Dirichlet (alpha, theta) stationary distribution. We derive a dual process representation for the diffusion, sugges
The Poisson--Dirichlet distribution arises in many different areas. The parameter $theta$ in the distribution is the scaled mutation rate of a population in the context of population genetics. The limiting case of $theta$ approaching infinity is prac
In this paper we give a central limit theorem for the weighted quadratic variations process of a two-parameter Brownian motion. As an application, we show that the discretized quadratic variations $sum_{i=1}^{[n s]} sum_{j=1}^{[n t]} | Delta_{i,j} Y