A two-parameter family of measure-valued diffusions with Poisson-Dirichlet stationary distributions

DOI10.1214/21-AAP1732zbMath1496.60097arXiv2007.05250MaRDI QIDQ2170375

Quan Shi, Douglas Rizzolo, Matthias Winkel, Noah Mills Forman

Publication date: 5 September 2022

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2007.05250

zbMATH Keywords

Fleming-Viot processexcursion theorystable processPoisson-Dirichlet distributioninfinitely-many-neutral-alleles model

Mathematics Subject Classification ID

Diffusion processes (60J60) Self-similar stochastic processes (60G18) Stable stochastic processes (60G52) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items (4)

Diffusions on a space of interval partitions: the two-parameter model ⋮ Unnamed Item ⋮ The leftmost column of ordered Chinese restaurant process up-down chains: intertwining and convergence ⋮ Ranked masses in two-parameter Fleming–Viot diffusions

Cites Work

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• The birth process with immigration, and the genealogical structure of large populations
• Some diffusion processes associated with two parameter Poisson-Dirichlet distribution and Dirichlet process
• A note on superprocesses
• Two-parameter family of infinite-dimensional diffusions on the Kingman simplex
• On Lévy processes conditioned to stay positive
• Stochastic partial differential equations for some measure-valued diffusions
• A stochastic equation based on a Poisson system for a class of measure- valued diffusion processes
• Continuity of a class of random time trnsformations
• The two-parameter Poisson-Dirichlet distribution derived from a stable subordinator
• Normalized excursion, meander and bridge for stable Lévy processes
• A survey and some generalizations of Bessel processes
• Exit problems for spectrally negative Lévy processes and applications to (Canadized) Russian options
• Uniform control of local times of spectrally positive stable processes
• Bayesian nonparametrics
• Alpha-diversity processes and normalized inverse-Gaussian diffusions
• Wright-Fisher diffusion with negative mutation rates
• Squared Bessel processes of positive and negative dimension embedded in Brownian local times
• Diffusions on a space of interval partitions: construction from marked Lévy processes
• Diffusions on a space of interval partitions: Poisson-Dirichlet stationary distributions
• A Ray-Knight representation of up-down Chinese restaurants
• A dynamic model for the two-parameter Dirichlet process
• Wright-Fisher construction of the two-parameter Poisson-Dirichlet diffusion
• Distributions of linear functionals of two parameter Poisson-Dirichlet random measures
• Measurable sets of measures
• Random Measures, Theory and Applications
• Measure-Valued Branching Markov Processes
• The infinitely-many-neutral-alleles diffusion model
• A decomposition of Bessel Bridges
• Fleming–Viot Processes in Population Genetics
• An Introduction to the Theory of Point Processes
• A family of densities derived from the three-parameter Dirichlet process
• Sur certains processus de lévy conditionnés à rester positifs
• An Introduction to the Theory of Point Processes

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