日本語フィールド
著者：Kenji Handa題名：The two-parameter Poisson-Dirichlet point process発表情報：Bernoulli 巻: 15 号: 4 ページ: 1082-1116キーワード：correlation function, Markov-Krein identity, point process, Poisson-Dirichlet distribution概要：PitmanとYorが導入した２パラメータPoisson-Dirichlet分布についてランダム測度の観点から解析した結果，確率母関数の表示から様々な密度公式や極限定理が導かれることがわかった．抄録：The two-parameter Poisson-Dirichlet distribution is a probability distribution on the totality of positive decreasing sequences with sum 1 and hence considered to govern masses of a random discrete distribution. A characterization of the associated point process (i.e., the random point process obtained by regarding the masses as points in the positive real line)
is given in terms of the correlation functions. Relying on this, we apply the theory of point processes to reveal mathematical structure of
the two-parameter Poisson-Dirichlet distribution. Also, developing the Laplace transform approach due to Pitman and Yor, we will be able to extend several results previously known for the one-parameter case, and the Markov-Krein identity for the generalized Dirichlet process is discussed from a point of view of functional analysis based on the two-parameter Poisson-Dirichlet distribution.英語フィールド
Author：Kenji HandaTitle：The two-parameter Poisson-Dirichlet point processAnnouncement information:Bernoulli Vol: 15 Issue: 4 Page: 1082-1116Keyword：correlation function, Markov-Krein identity, point process, Poisson-Dirichlet distributionAn abstract：The two-parameter Poisson-Dirichlet distribution is a probability distribution on the totality of positive decreasing sequences with sum 1 and hence considered to govern masses of a random discrete distribution. A characterization of the associated point process (i.e., the random point process obtained by regarding the masses as points in the positive real line)
is given in terms of the correlation functions. Relying on this, we apply the theory of point processes to reveal mathematical structure of
the two-parameter Poisson-Dirichlet distribution. Also, developing the Laplace transform approach due to Pitman and Yor, we will be able to extend several results previously known for the one-parameter case, and the Markov-Krein identity for the generalized Dirichlet process is discussed from a point of view of functional analysis based on the two-parameter Poisson-Dirichlet distribution.