2000/05/31 by N. Tsilevich, Н. В. Цилевич, A. M. Vershik +6
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Mathematics #Mathematical Approximation and Integration #Probability (math.PR) #Representation Theory (math.RT) #math.PR #math.RT
paper · pdf · doi:10.48550/arxiv.math/0005287
Prepublication du Laboratoire de Probabilites et Modeles Aleatoires, no. 575, Mars 2000
arxiv created 2000/05/31 · openalex publication_date 2000/05/31 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study fundamental properties of the gamma process and their relation to various topics such as Poisson-Dirichlet measures and stable processes. We prove the quasi-invariance of the gamma process with respect to a large group of linear transformations. We also show that it is a renormalized limit of the stable processes and has an equivalent sigma-finite measure (quasi-Lebesgue) with important invariance properties. New properties of the gamma process can be applied to the Poisson-Dirichlet measures. We also emphasize the deep similarity between the gamma process and the Brownian motion. The connection of the above topics makes more transparent some old and new facts about stable and gamma processes, and the Poisson-Dirichlet measures.