General criteria for the study of quasi-stationarity

DOI10.1214/22-ejp880arXiv1712.08092MaRDI QIDQ6164925

Nicolas Champagnat, Denis Villemonais

Publication date: 4 July 2023

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

Full work available at URL: https://arxiv.org/abs/1712.08092

zbMATH Keywords

quasi-stationary distributionmixing propertyQ-processdiscrete-time and continuous time Markov processesMarkov process with absorption

Mathematics Subject Classification ID

Continuous-time Markov processes on general state spaces (60J25) Discrete-time Markov processes on general state spaces (60J05) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Ergodicity, mixing, rates of mixing (37A25) Convergence of probability measures (60B10)

Related Items (14)

Transcritical bifurcation for the conditional distribution of a diffusion process ⋮ On quasi-stationaries for symmetric Markov processes ⋮ Coupled quantum harmonic oscillators and Feynman-Kac path integrals for linear diffusive particles ⋮ Self-similar solution for fractional Laplacian in cones ⋮ Quasi-equilibria and click times for a variant of Muller's ratchet ⋮ Large deviation principle for quasi-stationary distributions and multiscale dynamics of absorbed singular diffusions ⋮ On the stability of positive semigroups ⋮ Wasserstein contraction and Poincaré inequalities for elliptic diffusions with high diffusivity ⋮ Quasi-stationary behavior for a piecewise deterministic Markov model of chemostat: the Crump-Young model ⋮ Exponential quasi-ergodicity for processes with discontinuous trajectories ⋮ Impact of demography on extinction/fixation events ⋮ Mini-workshop: Entropy, information and control. Abstracts from the mini-workshop held March 4--10, 2018 ⋮ Sharp asymptotics of the first exit point density ⋮ Persistence exponents via perturbation theory: AR(1)-processes

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Conditions for the existence of quasi-stationary distributions for birth-death processes with killing
• On Dirichlet eigenvectors for neutral two-dimensional Markov chains
• Competitive or weak cooperative stochastic Lotka-Volterra systems conditioned on non-extinc\-tion
• Quasi-stationary distributions for structured birth and death processes with mutations
• Quasilimiting behavior for one-dimensional diffusions with killing
• Theoretical properties of quasi-stationary Monte Carlo methods
• Simulation of stopped diffusions
• Markov mortality models: implications of quasistationarity and varying initial distributions
• Quasi-stationary distributions for a class of discrete-time Markov chains
• Survival in a quasi-death process
• Uniform conditional ergodicity and intrinsic ultracontractivity
• Some penalisations of the Wiener measure
• Explicit and almost explicit spectral calculations for diffusion operators
• Quasi-stationary distributions and diffusion models in population dynamics
• First eigenvalue of one-dimensional diffusion processes
• Limit theorems for conditioned multitype Dawson-Watanabe processes and Feller diffusions
• On the convergence of diffusion processes conditioned to remain in a bounded region for large time to limiting positive recurrent diffusion processes
• Ultracontractivity and the heat kernel for Schrödinger operators and Dirichlet Laplacians
• Killed diffusions and their conditioning
• Asymptotic behavior of multitype Galton-Watson processes
• Stochastic approximation of quasi-stationary distributions on compact spaces and applications
• \(R\)-positivity, quasi-stationary distributions and ratio limit theorems for a class of probabilistic automata
• Asymptotic behavior of absorbing Markov chains conditional on nonabsorption for applications in conservation biology
• Weak approximation of killed diffusion using Euler schemes.
• Classification of killed one-dimensional diffusions.
• Existence of quasi-stationary distributions: A renewal dynamical approach
• Asymptotic laws for one-dimensional diffusions conditioned to nonabsorption
• Sharp bounds for the first eigenvalue of symmetric Markov processes and their applications
• Quasi-stationary distributions and population processes
• Absorbing boundaries and optimal stopping in a stochastic differential equation
• Quasistationary distributions for one-dimensional diffusions with singular boundary points
• Lyapunov criteria for uniform convergence of conditional distributions of absorbed Markov processes
• Convergence to quasi-stationarity through Poincaré inequalities and Bakry-Émery criteria
• More on the long time stability of Feynman-Kac semigroups
• Unique quasi-stationary distribution, with a possibly stabilizing extinction
• Practical criteria for \(R\)-positive recurrence of unbounded semigroups
• On time scales and quasi-stationary distributions for multitype birth-and-death processes
• Persistence of one-dimensional AR(1)-sequences
• Existence and uniqueness of quasi-stationary distributions for symmetric Markov processes with tightness property
• Quasi-stationary distributions for discrete-state models
• The \(\lambda\)-invariant measures of subcritical Bienaymé-Galton-Watson processes
• Exponential mixing properties for time inhomogeneous diffusion processes with killing
• Quasi-stationary distributions for randomly perturbed dynamical systems
• Quasi-stationary distributions and the continuous-state branching process conditioned to be never extinct
• Minimal quasi-stationary distribution approximation for a birth and death process
• Ergodic properties of nonnegative matrices. I
• On multitype branching processes with \(\rho\leq1\)
• Multidimensional diffusion processes.
• Exponential convergence to quasi-stationary distribution and \(Q\)-process
• Sharp asymptotics for the quasi-stationary distribution of birth-and-death processes
• Mean Field Simulation for Monte Carlo Integration
• Ultracontractivity for Markov Semigroups and Quasi-Stationary Distributions
• Yet Another Look at Harris’ Ergodic Theorem for Markov Chains
• Mixed-mode oscillations and interspike interval statistics in the stochastic FitzHugh–Nagumo model
• Quasi-Stationary Distributions
• Existence and Uniqueness of a Quasistationary Distribution for Markov Processes with Fast Return from Infinity
• Exponential convergence to quasi-stationary distribution for absorbed one-dimensional diffusions with killing
• Stability of Markovian processes III: Foster–Lyapunov criteria for continuous-time processes
• Uniqueness of Quasistationary Distributions and Discrete Spectra when ∞ is an Entrance Boundary and 0 is Singular
• Extensions of Jentzsch's Theorem
• On asymptotic behaviour of probabilities in groups of states of homogeneous Markov chain
• The Classification of Birth and Death Processes
• Piecewise deterministic Markov process — recent results
• Markov Chains and Stochastic Stability
• Some results for quasi-stationary distributions of birth-death processes
• Quasi-stationary distributions and convergence to quasi-stationarity of birth-death processes
• Existence of non-trivial quasi-stationary distributions in the birth-death chain
• Martingale Transforms
• Quasi-stationary distributions of birth-and-death processes
• Domain of attraction of the quasi-stationary distributions for the Ornstein-Uhlenbeck process
• Euler schemes and half-space approximation for the simulation of diffusion in a domain
• Spectral Theory for Random Poincaré Maps
• Uniform convergence of penalized time-inhomogeneous Markov processes
• Criteria for Exponential Convergence to Quasi-Stationary Distributions and Applications to Multi-Dimensional Diffusions
• Uniform convergence of conditional distributions for absorbed one-dimensional diffusions
• Extinction Probability in A Birth-Death Process with Killing
• On Quasi-Stationary distributions in absorbing discrete-time finite Markov chains
• On quasi-stationary distributions in discrete-time Markov chains with a denumerable infinity of states
• The Exponential Decay of Markov Transition Probabilities
• On quasi-stationary distributions in absorbing continuous-time finite Markov chains
• An $L^p$-Convergence Theorem
• The limiting behavior of transient birth and death processes conditioned on survival
• Spectral theory of semi-groups connected with diffusion processes and its application
• A law of large numbers for branching Markov processes by the ergodicity of ancestral lineages
• Transcritical bifurcation for the conditional distribution of a diffusion process
• A non‐conservative Harris ergodic theorem

This page was built for publication: General criteria for the study of quasi-stationarity