Continuous-state branching processes with competition: duality and reflection at infinity

DOI10.1214/19-EJP299zbMath1412.60127arXiv1711.06827WikidataQ114060542 ScholiaQ114060542MaRDI QIDQ2631859

Clément Foucart

Publication date: 16 May 2019

Published in: Electronic Journal of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1711.06827

zbMATH Keywords

dualityexplosionentrance boundaryreflecting boundarycontinuous-state branching processcoming down from infinitygeneralized Feller diffusionbranching process with interactionLamperti's time change

Mathematics Subject Classification ID

Population dynamics (general) (92D25) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80) Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) (60J70)

Related Items (11)

On the extinction of continuous state branching processes with competition ⋮ On the explosion of the number of fragments in simple exchangeable fragmentation-coagulation processes ⋮ Extinction time and the total mass of the continuous-state branching processes with competition ⋮ On the boundary classification of \(\Lambda\)-Wright-Fisher processes with frequency-dependent selection ⋮ Extinction time of logistic branching processes in a Brownian environment ⋮ On the entrance at infinity of Feller processes with no negative jumps ⋮ Continuous-state branching processes with collisions: first passage times and duality ⋮ Explosion of continuous-state branching processes with competition in a Lévy environment ⋮ Extinction and coming down from infinity of continuous-state branching processes with competition in a Lévy environment ⋮ Branching processes with interactions: subcritical cooperative regime ⋮ A phase transition in the coming down from infinity of simple exchangeable fragmentation-coagulation processes

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Self-similar scaling limits of Markov chains on the positive integers
• The branching process with logistic growth
• A phase transition in excursions from infinity of the ``fast fragmentation-coalescence process
• Interacting particle systems. With a new postface.
• Operator-selfdecomposable distributions as limit distributions of processes of Ornstein-Uhlenbeck type
• Weak convergence to a Markov chain with an entrance boundary: Ancestral processes in population genetics
• Branching processes with interaction and a generalized Ray-Knight theorem
• Proof(s) of the Lamperti representation of continuous-state branching processes
• Quasi-stationary distributions and diffusion models in population dynamics
• A duality relation for entrance and exit laws for Markov processes
• A recurrence criterion for Markov processes of Ornstein-Uhlenbeck type
• On the convergence of sequences of branching processes
• Ray-Knight representation of flows of branching processes with competition by pruning of Lévy trees
• Exchangeable fragmentation-coalescence processes and their equilibrium measures
• On stationary distributions for the KPP equation with branching noise
• ``Trees under attack: a Ray-Knight representation of Feller's branching diffusion with logistic growth
• Fluctuations of Lévy processes with applications. Introductory lectures
• Ergodic behavior of locally regulated branching populations
• On a martingale associated to generalized Ornstein-Uhlenbeck processes and an application to finance
• Probabilistic Models of Population Evolution
• Asymptotic behaviour of continuous time, continuous state-space branching processes
• Stochastic Calculus
• The Limit of a Sequence of Branching Processes
• Stochastic branching processes with continuous state space
• Continuous state branching processes
• Diffusion Processes in One Dimension

This page was built for publication: Continuous-state branching processes with competition: duality and reflection at infinity