Poisson representations of branching Markov and measure-valued branching processes

DOI10.1214/10-AOP574zbMath1232.60053arXiv1104.1496MaRDI QIDQ533744

Eliane R. Rodrigues, Thomas G. Kurtz

Publication date: 6 May 2011

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

Full work available at URL: https://arxiv.org/abs/1104.1496

zbMATH Keywords

conditioningexchangeabilitysuperprocessrandom environmentsCox processparticle representationDawson-Watanabe processbranching Markov processFeller diffusionmeasure-valued diffusion

Mathematics Subject Classification ID

Continuous-time Markov processes on general state spaces (60J25) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Diffusion processes (60J60) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80) Superprocesses (60J68)

Related Items

Looking forwards and backwards: dynamics and genealogies of locally regulated populations ⋮ Evolving genealogies for branching populations under selection and competition ⋮ Spine for interacting populations and sampling ⋮ Measure-valued continuous curves and processes in total variation norm ⋮ Change of measure in the lookdown particle system ⋮ Genealogical constructions and asymptotics for continuous-time Markov and continuous-state branching processes ⋮ Genealogical constructions of population models ⋮ The spatial lambda-Fleming-Viot process: an event-based construction and a lookdown representation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Asymptotic behavior of the measure-valued branching process with immigration
• The Markov branching-castastrophe process
• Limit theorems for the population size of a birth and death process allowing catastrophes
• Construction and regularity of measure-valued Markov branching processes
• Minimal conditions for weak convergence to a diffusion process on the line
• Weak limit theorems for stochastic integrals and stochastic differential equations
• Measure-valued branching processes with immigration
• Stochastic evolution equations and related measure processes
• Extinction and exponential growth in random environments
• On the convergence of sequences of branching processes
• The non-degenerate limit for supercritical branching diffusions
• Brillinger type mixing conditions for a simple branching diffusion process
• Martingale problems for conditional distributions of Markov processes
• On transition semigroups of \((A,\mathbf\Psi)\)-superprocesses with immigration
• Genealogical processes for Fleming-Viot models with selection and recombination
• Particle representations for a class of nonlinear SPDEs
• Particle representations for measure-valued population models
• A necessary and sufficient condition for the \(\Lambda\)-coalescent to come down from the infinity
• The \(\Lambda \)-coalescent speed of coming down from infinity
• Stochastic flows associated to coalescent processes. III: Limit theorems
• A limit theorem of branching processes and continuous state branching processes
• Branching Markov processes. I
• Branching Markov processes. II
• Branching Markov processes. III
• A limit theorem for perturbed operator semigroups with applications to random evolutions
• A countable representation of the Fleming-Viot measure-valued diffusion
• Measure-valued Markov branching processes conditioned on non-extinction
• The multitype measure branching process
• Weak convergence of sequences of semimartingales with applications to multitype branching processes
• The Markov branching process with density-independent catastrophes I. Behaviour of extinction probabilities
• Supercritical branching processes with density independent catastrophes
• Asymptotic results for the extinction time of Markov branching processes allowing emigration, I. Random walk decrements
• On the functional central limit theorem and the law of the iterated logarithm for Markov processes
• The Markov branching process with density-independent catastrophes. II. The subcritical and critical cases
• Two representations of a conditioned superprocess
• Weighted Occupation Time for Branching Particle Systems and a Representation for the Supercritical Superprocess
• The Markov branching process with density-independent catastrophes. III. The supercritical case
• On branching Markov processes
• Stationary solutions and forward equations for controlled and singular martingale problems