Lyapunov exponents for branching processes in a random environment: the effect of information

DOI10.1007/s10955-016-1474-3zbMath1341.60105arXiv1411.7531OpenAlexW1415798537WikidataQ46116076 ScholiaQ46116076MaRDI QIDQ300710

Guy Latouche, Sophie Hautphenne

Publication date: 28 June 2016

Published in: Journal of Mathematical Biology, Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1411.7531

zbMATH Keywords

demographybranching processesrandom matricesLyapunov exponentsmatrix analytic methodsmultitype branching processesextinction criterionMarkovian random environmentfamily treesMarkovian models

Mathematics Subject Classification ID

Computational methods in Markov chains (60J22) Random matrices (probabilistic aspects) (60B20) Applications of branching processes (60J85) Population dynamics (general) (92D25) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Processes in random environments (60K37) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80) Mathematical geography and demography (91D20) Continuous-time Markov processes on discrete state spaces (60J27)

Related Items

An \textit{EM} algorithm for the model fitting of Markovian binary trees ⋮ A subordinated Markov model for stochastic mortality ⋮ A Structured Markov Chain Approach to Branching Processes ⋮ Efficient Implementations of the EM-Algorithm for Transient Markovian Arrival Processes ⋮ How old is this bird? The age distribution under some phase sampling schemes ⋮ Cause-of-death mortality: what can be learned from population dynamics? ⋮ How can a cause-of-death reduction be compensated for by the population heterogeneity? A dynamic approach ⋮ A branching process model for dormancy and seed banks in randomly fluctuating environments ⋮ Fitting Markovian binary trees using global and individual demographic data

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Algorithmic approach to the extinction probability of branching processes
• Lower bounds for the maximal Lyapunov exponent
• Newton's iteration for the extinction probability of a Markovian binary tree
• Markovian trees: Properties and algorithms
• Maximal Lyapunov exponents for random matrix products
• Differential equation approximations for Markov chains
• Computable examples of the maximal Lyapunov exponent
• Subadditive ergodic theory
• Evolutionary formalism for products of positive random matrices
• The Lyapunov exponent and joint spectral radius of pairs of matrices are hard - when not impossible - to compute and to approximate
• Transient Markov arrival processes
• On the notion(s) of duality for Markov processes
• Non-negative matrices and Markov chains.
• Markovian Trees Subject to Catastrophes: Would They Survive Forever?
• Supercritical multitype branching processes: the ancestral types of typical individuals
• Erlangian Approximations for Finite-Horizon Ruin Probabilities
• Marked point processes as limits of Markovian arrival streams
• Erlangized Fluid Queues with Application To Uncontrolled Fire Perimeter
• On multitype branching processes in a random environment
• Recurrence and transience of random walks in random environments on a strip