A law of large numbers for branching Markov processes by the ergodicity of ancestral lineages

DOI10.1051/ps/2018029zbMath1506.60097arXiv1707.07993OpenAlexW2963118919WikidataQ128652451 ScholiaQ128652451MaRDI QIDQ5881042

Aline Marguet

Publication date: 9 March 2023

Published in: ESAIM: Probability and Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1707.07993

zbMATH Keywords

ergodicitylaw of large numbersbranching Markov processestime-inhomogeneous Markov process

Mathematics Subject Classification ID

Strong limit theorems (60F15) Applications of branching processes (60J85) Population dynamics (general) (92D25) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

Related Items (14)

Periodic asymptotic dynamics of the measure solutions to an equal mitosis equation ⋮ Dynamics of lineages in adaptation to a gradual environmental change ⋮ A non‐conservative Harris ergodic theorem ⋮ A growth-fragmentation-isolation process on random recursive trees and contact tracing ⋮ General criteria for the study of quasi-stationarity ⋮ Time reversal of spinal processes for linear and non-linear branching processes near stationarity ⋮ On the stability of positive semigroups ⋮ Spread of parasites affecting death and division rates in a cell population ⋮ The strong Malthusian behavior of growth-fragmentation processes ⋮ Long-time behavior and Darwinian optimality for an asymmetric size-structured branching process ⋮ Uniform sampling in a structured branching population ⋮ On a Feynman-Kac approach to growth-fragmentation semigroups and their asymptotic behaviors ⋮ A probabilistic view on the long-time behaviour of growth-fragmentation semigroups with bounded fragmentation rates ⋮ Central limit theorem for bifurcating Markov chains under pointwise ergodic conditions

Cites Work

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• Weak law of large numbers for some Markov chains along non homogeneous genealogies
• Yet Another Look at Harris’ Ergodic Theorem for Markov Chains
• Strong limit theorems for general supercritical branching processes with applications to branching diffusions
• Some limit theorems for positive recurrent branching Markov chains: I
• Some limit theorems for positive recurrent branching Markov chains: II
• Supercritical multitype branching processes: the ancestral types of typical individuals
• Limit theorems for some branching measure-valued processes

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