A stochastic approximation approach to quasi-stationary distributions on finite spaces
Michel Benaïm,Bertrand Cloez +1 more
Reads0
Chats0
TLDR
In this article, a stochastic approximation algorithm for the simulation of quasi-stationary distributions on finite state spaces has been proposed, which is a generalization of a method introduced by Aldous, Flannery and Palacios.Abstract:
This work is concerned with the analysis of a stochastic approximation algorithm for the simulation of quasi-stationary distributions on finite state spaces. This is a generalization of a method introduced by Aldous, Flannery and Palacios. It is shown that the asymptotic behavior of the empirical occupation measure of this process is precisely related to the asymptotic behavior of some deterministic dynamical system induced by a vector field on the unit simplex. This approach provides new proof of convergence as well as precise asymptotic rates for this type of algorithm. In the last part, our convergence results are compared with those of a particle system algorithm (a discrete-time version of the Fleming-Viot algorithm).read more
Citations
More filters
Journal ArticleDOI
Perspectives in Mathematical Modelling for Microbial Ecology
Matthew J. Wade,Jérôme Harmand,Boumediene Benyahia,Théodore Bouchez,Stephane Chaillou,Bertrand Cloez,Jean-Jacques Godon,Claude Lobry,Boumédiène Moussa Boubjemaa,Alain Rapaport,Tewfik Sari,Roger Arditi +11 more
TL;DR: In this paper, the current state of mathematical modelling in microbial ecology, looking back at the developments that have defined the synergies between the disciplines, and outline some of the existing challenges that motivate us to provide practical models in the hope that greater engagement with empiricists and practitioners in the microbiological domain may be achieved.
Journal ArticleDOI
Analysis of a stochastic approximation algorithm for computing quasi-stationary distributions
TL;DR: In this paper, the convergence properties of a Monte Carlo estimator proposed in the physics literature to compute the quasi-stationary distribution on a transient set of a Markov chain are studied.
Posted Content
Stochastic approximation of quasi-stationary distributions on compact spaces and applications
TL;DR: In this paper, a recursive algorithm for the approximation of the quasi-stationary distribution of a general Markov chain living on a compact metric space was proposed and analyzed for the non-irreducible case.
Journal ArticleDOI
Quasistationary distributions for one-dimensional diffusions with singular boundary points
Alexandru Hening,Martin Kolb +1 more
TL;DR: In this paper, the existence of quasistationary distributions for diffusions on ( 0, ∞ ) allowing singular behavior at 0 and ∞ was characterized and it was shown that there exists such a distribution as soon as the spectrum of the generator is strictly positive.
Posted ContentDOI
Does deterministic coexistence theory matter in a finite world? Insights from serpentine annual plants
TL;DR: The results tend to support the informed use of deterministic theory for understanding the duration of species coexistence, while highlighting the need to incorporate information on species’ equilibrium population sizes in addition to invasion growth rates.
References
More filters
Book
The Theory of Matrices
TL;DR: In this article, the Routh-Hurwitz problem of singular pencils of matrices has been studied in the context of systems of linear differential equations with variable coefficients, and its applications to the analysis of complex matrices have been discussed.
BookDOI
Adaptive Algorithms and Stochastic Approximations
TL;DR: The juxtaposition of these two expressions in the title reflects the ambition of the authors to produce a reference work, both for engineers who use adaptive algorithms and for probabilists or statisticians who would like to study stochastic approximations in terms of problems arising from real applications.
Journal ArticleDOI
A survey of random processes with reinforcement
TL;DR: The models surveyed in this paper include generalized Polya urns, reinforced random walks, interacting urn models, and continuous reinforced processes, with a focus on methods and results, with sketches provided of some proofs.
Book ChapterDOI
Dynamics of stochastic approximation algorithms
TL;DR: These notes were written for a D.E.A. course given at Ecole Normale Superieure de Cachan and University Toulouse III to introduce the reader to the dynamical system aspects of the theory of stochastic approximations.
Journal ArticleDOI
On Quasi-Stationary distributions in absorbing discrete-time finite Markov chains
J. N. Darroch,Eugene Seneta +1 more
TL;DR: In this article, the authors show that the time to absorption from the set T of transient states of a Markov chain may be sufficiently long for the probability distribution over T to settle down in some sense to a quasi-stationary distribution.
Related Papers (5)
Quasi Stationary Distributions and Fleming-Viot Processes in Countable Spaces
Pablo A. Ferrari,Nevena Maric +1 more