2016/01/22 by Dario Spanò, Spanò, Dario, Antonio Lijoi +1
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #60G51 #60G57 #62F15 #Bayesian Methods and Mixture Models #Classical Analysis and ODEs (math.CA) #Diffusion and Search Dynamics #FOS: Mathematics #Probability (math.PR) #Statistics Theory (math.ST) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1601.06079
openalex publication_date 2016/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The present paper provides a characterisation of exchangeable pairs of random measures (\widetildeμ1,\widetildeμ2) whose identical margins are fixed to coincide with the distribution of a gamma completely random measure, and whose dependence structure is given in terms of canonical correlations. It is first shown that canonical correlation sequences for the finite-dimensional distributions of (\widetildeμ1,\widetildeμ2) are moments of means of a Dirichlet process having random base measure. Necessary and sufficient conditions are further given for canonically correlated gamma completely random measures to have independent joint increments. Finally, time-homogeneous Feller processes with gamma reversible measure and canonical autocorrelations are characterised as Dawson--Watanabe diffusions with independent homogeneous immigration, time-changed via an independent subordinator. It is thus shown that Dawson--Watanabe diffusions subordinated by pure drift are the only processes in this class whose time-finite-dimensional distributions have, jointly, independent increments.