Concentration of quasi-stationary distributions for one-dimensional diffusions with applications

DOI10.1214/23-aihp1362zbMATH Open1546.60149MaRDI QIDQ6596219

Zhongwei Shen, Shirou Wang, Yingfei Yi

Publication date: 2 September 2024

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

zbMATH Keywords

diffusion approximationtightnesstransient statequasi-stationary distributionone-dimensional diffusion processbirth-and-death processconcentrationtransient dynamicsKeizer's paradox

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Population dynamics (general) (92D25) Diffusion processes (60J60) Ordinary differential equations and systems with randomness (34F05) Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) (60J70)

Cites Work

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• Slow manifold reduction of a stochastic chemical reaction: exploring Keizer's paradox
• Competitive or weak cooperative stochastic Lotka-Volterra systems conditioned on non-extinc\-tion
• Stochastic stability of differential equations. With contributions by G. N. Milstein and M. B. Nevelson
• Quasilimiting behavior for one-dimensional diffusions with killing
• Existence and construction of quasi-stationary distributions for one-dimensional diffusions
• Quasi-stationary distributions and diffusion models in population dynamics
• On the quasi-stationary distribution of a stochastic Ricker model
• On the quasi-stationary distribution for some randomly perturbed transformations of an interval
• Elliptic partial differential equations of second order
• The quasi-stationary distribution for small random perturbations of certain one-dimensional maps
• Classification of killed one-dimensional diffusions.
• Existence of quasi-stationary distributions: A renewal dynamical approach
• Asymptotic laws for one-dimensional diffusions conditioned to nonabsorption
• Quasi-stationary distributions and population processes
• Quasistationary distributions for one-dimensional diffusions with singular boundary points
• Lyapunov criteria for uniform convergence of conditional distributions of absorbed Markov processes
• The exit from a metastable state: concentration of the exit point distribution on the low energy saddle points. II
• The exit from a metastable state: concentration of the exit point distribution on the low energy saddle points. I
• Sharp asymptotics of the first exit point density
• Low temperature asymptotics for quasistationary distributions in a bounded domain
• Integral identity and measure estimates for stationary Fokker-Planck equations
• A quasistationary analysis of a stochastic chemical reaction: Keizer's paradox
• Quasi-stationary distributions for randomly perturbed dynamical systems
• Exponential convergence to quasi-stationary distribution and \(Q\)-process
• Sharp asymptotics for the quasi-stationary distribution of birth-and-death processes
• The parabolic differential equations and the associated semigroups of transformation
• Ultracontractivity for Markov Semigroups and Quasi-Stationary Distributions
• Quasi-Stationary Distributions
• Exponential convergence to quasi-stationary distribution for absorbed one-dimensional diffusions with killing
• Nonlinear stochastic dynamics of mesoscopic homogeneous biochemical reaction systems—an analytical theory
• Random Perturbations of Dynamical Systems
• Uniqueness of Quasistationary Distributions and Discrete Spectra when ∞ is an Entrance Boundary and 0 is Singular
• Quasistationary distributions for one-dimensional diffusions with killing
• Markov Chains and Stochastic Stability
• Recent progress on the small parameter exit problem^†
• Quasi-stationary distributions of birth-and-death processes
• Quasi-stationary distributions for a Brownian motion with drift and associated limit laws
• Domain of attraction of the quasi-stationary distributions for the Ornstein-Uhlenbeck process
• Nonlinear Systems Analysis
• Limiting conditional and conditional invariant distributions for the Poisson process with negative drift
• A unifying approach to non-minimal quasi-stationary distributions for one-dimensional diffusions
• Uniform convergence of conditional distributions for absorbed one-dimensional diffusions
• Stochastic Analysis of Biochemical Systems
• Random Perturbations of Dynamical Systems with Absorbing States
• Limit theorems for sequences of jump Markov processes approximating ordinary differential processes
• Spectral theory of semi-groups connected with diffusion processes and its application
• Diffusion Processes in One Dimension

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