Strong laws of large numbers for a growth-fragmentation process with bounded cell sizes

zbMath1505.60080arXiv2012.03273MaRDI QIDQ5870417

Publication date: 9 January 2023

Full work available at URL: https://arxiv.org/abs/2012.03273

spectral radius law of large numbers spectral gap cell division ergodic theorem growth-fragmentation asynchronous exponential growth spectrally negative Lévy process skeleton decomposition intrinsic martingale dividend process

Mathematics Subject Classification ID

One-parameter semigroups and linear evolution equations (47D06) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Ergodic theorems, spectral theory, Markov operators (37A30) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

Related Items (1)

A growth-fragmentation-isolation process on random recursive trees and contact tracing

Cites Work

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Spectral analysis of semigroups and growth-fragmentation equations
Links between deterministic and stochastic approaches for invasion in growth-fragmentation-death models
Asymptotics of self-similar growth-fragmentation processes
Markovian growth-fragmentation processes
Limit theorems for Markov processes indexed by continuous time Galton-Watson trees
Spines, skeletons and the strong law of large numbers for superdiffusions
Strong law of large numbers for branching diffusions
On the perturbation theory for strongly continuous semigroups
A probabilistic approach to spectral analysis of growth-fragmentation equations
On the variations of the principal eigenvalue with respect to a parameter in growth-fragmentation models
Asynchronous exponential growth of a general structured population model
Asynchronous exponential growth of the growth-fragmentation equation with unbounded fragmentation rate
The strong Malthusian behavior of growth-fragmentation processes
Stochastic methods for the neutron transport equation. II: Almost sure growth
On a family of critical growth-fragmentation semigroups and refracted Lévy processes
Multi-species neutron transport equation
Uniform sampling in a structured branching population
On a Feynman-Kac approach to growth-fragmentation semigroups and their asymptotic behaviors
Fluctuations of Lévy processes with applications. Introductory lectures
Existence and uniqueness of nonnegative eigenfunctions of the Boltzmann operator
General relative entropy inequality: an illustration on growth models
Exponential convergence to quasi-stationary distribution and \(Q\)-process
Spectral Gap for the Growth-Fragmentation Equation via Harris's Theorem
A Spine Approach to Branching Diffusions with Applications to L p -Convergence of Martingales
Strong limit theorems for general supercritical branching processes with applications to branching diffusions
Relative Entropy Method for Measure Solutions of the Growth-Fragmentation Equation
Probabilistic and Piecewise Deterministic models in Biology
Statistical Inference for Piecewise‐deterministic Markov Processes
Applied Probability and Queues
Probabilistic aspects of critical growth-fragmentation equations
Exponential convergence rate of ruin probabilities for level-dependent Lévy-driven risk processes

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