Minimal quasi-stationary distribution approximation for a birth and death process
Reads0
Chats0
TLDR
In this paper, the authors prove a Lyapunov-type criterion for the positive recurrence of absorbed birth and death processes and provide new results on the domain of attraction of the minimal quasi-stationary distribution.Abstract:
In a first part, we prove a Lyapunov-type criterion for the $\xi_1$-positive recurrence of absorbed birth and death processes and provide new results on the domain of attraction of the minimal quasi-stationary distribution.
In a second part, we study the ergodicity and the convergence of a Fleming-Viot type particle system whose particles evolve independently as a birth and death process and jump on each others when they hit $0$. Our main result is that the sequence of empirical stationary distributions of the particle system converges to the minimal quasi-stationary distribution of the birth and death process.read more
Citations
More filters
Posted Content
General criteria for the study of quasi-stationarity
TL;DR: In this paper, the authors provide general criteria ensuring the existence and the exponential non-uniform convergence in total variation norm to a quasi-stationary distribution for Markov processes with absorption.
Journal ArticleDOI
Speed and fluctuations of N -particle branching Brownian motion with spatial selection
TL;DR: In this paper, the authors consider branching Brownian motion on the real line with the following selection mechanism: every time the number of particles exceeds a (large) given number N, only the rightmost particles are kept and the others killed.
Posted Content
A Non-Conservative Harris' Ergodic Theorem
TL;DR: In this article, the authors consider non-conservative positive semigroups and obtain necessary and sufficient conditions for uniform exponential contraction in weighted total variation norm, and obtain exponential convergence of birth and death processes conditioned on survival to their quasi-stationary distribution.
Journal ArticleDOI
Convergence of a non-failable mean-field particle system
TL;DR: In this paper, the authors introduce an original mean-field particle system, which is always well defined and whose large number particle limit is, in all generality, the distribution of a process conditioned to not hit a given set.
Posted Content
Convergence of the Fleming-Viot process toward the minimal quasi-stationary distribution
TL;DR: In this article, it was shown that the Fleming-Viot process selects the minimal quasi-stationary distribution for Markov processes with soft killing on non-compact state spaces.
References
More filters
Journal ArticleDOI
Stability of Markovian processes III: Foster–Lyapunov criteria for continuous-time processes
Sean P. Meyn,Richard L. Tweedie +1 more
TL;DR: In this paper, the authors developed criteria for continuous-parameter Markovian processes on general state spaces, based on Foster-Lyapunov inequalities for the extended generator, and applied the criteria to several specific processes, including linear stochastic systems under nonlinear feedback, work-modulated queues, general release storage processes and risk processes.
Journal ArticleDOI
Quasi-stationary distributions and population processes
Sylvie Méléard,Denis Villemonais +1 more
TL;DR: In this article, a survey of quasi-stationary distributions with a specific focus on models derived from ecology and population dynamics is presented, where general results on quasi-stability are given and examples developed in detail.
Journal ArticleDOI
Quasi-stationary distributions and convergence to quasi-stationarity of birth-death processes
TL;DR: In this article, the authors studied the quasi-stationary distribution of a birth-death process on the state space {−1, 0, 1, ·· ·}, where −1 is an absorbing state which is reached with certainty and {0, 1 · · ·} is an irreducible class.
Journal ArticleDOI
Exponential convergence to quasi-stationary distribution and Q-process
TL;DR: In this article, the authors obtain necessary and sufficient conditions for exponential convergence to a unique quasi-stationary distribution in the total variation norm of the $$Q$$ -process (the process conditioned to never be absorbed), and apply these results to one-dimensional birth and death processes with catastrophes, multi-dimensional and infinite-dimensional population models with Brownian mutations and neutron transport dynamics absorbed at the boundary of a bounded domain.
Related Papers (5)
Quasi Stationary Distributions and Fleming-Viot Processes in Countable Spaces
Pablo A. Ferrari,Nevena Maric +1 more