Open Access
Issue |
ESAIM: PS
Volume 27, 2023
|
|
---|---|---|
Page(s) | 867 - 912 | |
DOI | https://doi.org/10.1051/ps/2023016 | |
Published online | 31 October 2023 |
- E. Arjas, E. Nummelin and R.L. Tweedie, Semi-Markov processes on a general state space: α-theory and quasi-stationarity. J. Austral. Math. Soc. Ser. A 30 (1980) 187–200. [Google Scholar]
- M. Alfaro, P. Gabriel and O. Kavian, Confining integro-differential equations originating from evolutionary biology: ground states and long time dynamics. Discrete Cont. Dyn. Syst. B 28 (2023) 5905–5933. [CrossRef] [Google Scholar]
- R. Bürger, Perturbations of positive semigroups and applications to population genetics. Math. Z. 197 (1988) 259–272. [CrossRef] [MathSciNet] [Google Scholar]
- R. Bürger and I.M. Bomze, Stationary distributions under mutation-selection balance: structure and properties. Adv. Appl. Prob. 28 (1996) 227–251. [CrossRef] [Google Scholar]
- Bansaye, B. Cloez and P. Gabriel, Ergodic behavior of non-conservative semigroups via generalized Doeblin’s conditions. Proc. Acta Appl. Math. 166 (2019) 29–72. [Google Scholar]
- Bansaye, B. Cloez, P. Gabriel and A. Marguet, A non-conservative Harris’ ergodic theorem. J. London Math. Soc. 106 (2022) 2459–2510. [CrossRef] [MathSciNet] [Google Scholar]
- O. Bonnefon, J. Coville and G. Legendre, Concentration phenomenon in some non-local equation. Discrete Contin. Dyn. Syst.-B 22 (2017) 763–781. [Google Scholar]
- H. Berestycki, J. Coville and H.-H. Vo, Persistence criteria for populations with non-local dispersion. J. Math. Biol. 72 (2016) 1693–1745. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
- H. Berestycki, O. Diekmann, C.J. Nagelkerke and P.A. Zegeling, Can a species keep pace with a shifting climate?. Bull. Math. Biol. 71 (2009) 399–429. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
- H. Berestycki, F. Hamel and L. Roques, Analysis of the periodically fragmented environment model. I. Species persistence. J. Math. Biol. 51 (2005) 75–113. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
- H. Berestycki, F. Hamel and L. Roques, Reaction-diffusion equations for population dynamics with forced speed. I. The case of the whole space. Discrete Contin. Dyn. Syst.-B 21 (2008) 41–67. [CrossRef] [Google Scholar]
- H. Berestycki, F. Hamel and L. Roques, Reaction-diffusion equations for population dynamics with forced speed. II. Cylindrical- type domains. Discrete Contin. Dyn. Syst.-B 25 (2009) 19–61. [CrossRef] [Google Scholar]
- H. Berestycki, L. Nirenberg and S.R.S. Varadhan, The principal eigenvalue and maximum principle for second-order elliptic operators in general domains. Commun. Pure Appl. Math. XLVII (1994) 47–92. [CrossRef] [Google Scholar]
- T. Britton and E. Pardoux, Stochastic epidemic models with inference, Part I. Lecture Notes in Math. 2255 (2019). [CrossRef] [Google Scholar]
- J. Bertoin and A.-R. Watson, The strong Malthusian behavior of growth-fragmentation processes. Annales Henri Lebesgue 3 (2020) 795–823. [CrossRef] [MathSciNet] [Google Scholar]
- R.S. Cantrell and C. Cosner, On the effects of spatial heterogeneity on the persistence of interacting species. J. Math. Biol. 37 (1998) 103–145. [CrossRef] [MathSciNet] [Google Scholar]
- N. Champagnat, K.A. Coulibaly-Pasquier and D. Villemonais, Criteria for exponential convergence to quasi-stationary distributions and applications to multi-dimensional diffusions. Sémin. Probab. XLIX 2215 (2018) 165–182. [CrossRef] [Google Scholar]
- R. Chazottes, P. Collet and S. Méléard, On time scales and quasi-stationary distributions for multitype birth-and-death processes. Ann. Inst. H. Poincaré Prob. Stat. 55 (2019) 2249–2294. [CrossRef] [Google Scholar]
- N. Champagnat and D. Villemonais, Exponential convergence to quasi-stationary distribution and Q-process. Prob. Theory Rel. Fields 164 (2016) 243–283. [CrossRef] [Google Scholar]
- N. Champagnat and D. Villemonais, Exponential convergence to quasi-stationary distribution for absorbed one-dimensional diffusions with killing. ALEA - Lat. Am. J. Prob. Math. Stat. XIV (2017) 177–199. [CrossRef] [Google Scholar]
- N. Champagnat and D. Villemonais, Uniform convergence of conditional distributions for absorbed one-dimensional diffusions. Adv. Appl. Prob. 50 (2018) 178–203. [CrossRef] [Google Scholar]
- N. Champagnat and D. Villemonais, Uniform convergence of penalized time-inhomogeneous Markov processes. ESAIM: Prob. Stat. 22 (2018) 129–162. [CrossRef] [EDP Sciences] [Google Scholar]
- N. Champagnat and D. Villemonais, Lyapunov criteria for uniform convergence of conditional distributions of absorbed Markov processes. Stoch. Proc. Appl. 135 (2021) 51–74. [CrossRef] [Google Scholar]
- N. Champagnat and D. Villemonais, General criteria for the study of quasi-stationarity. Electron. J. Probab. 28 (2023) 1–84. [CrossRef] [Google Scholar]
- B. Cloez and P. Gabriel, On an irreducibility type condition for the ergodicity of nonconservative semigroups. Comptes Rendus. Mathématique 358 (2020) 733–742. [CrossRef] [MathSciNet] [Google Scholar]
- P. Collet, S. Martínez and J. San Martin, Quasi-Stationary Distributions, Probab. and Its Appl. Springer, Berlin Heidelberg (2013). [CrossRef] [Google Scholar]
- P. Collet, S. Martínez, S. Méléard and J. San Martín, Quasi-stationary distributions for structured birth and death processes with mutations. Prob. Theory Rel. Fields 151 (2011) 191–231. [CrossRef] [Google Scholar]
- J. Coville, On a simple criterion for the existence of a principal eigenfunction of some nonlocal operators. J. Differ. Equ. 249 (2010) 2921–2953. [CrossRef] [Google Scholar]
- J. Coville, Singular measure as principal eigenfunction of some nonlocal operators. Appl. Math. Lett. 26 (2013) 831–835. [CrossRef] [MathSciNet] [Google Scholar]
- J. Coville, J. Dávila and S. Martínez, Existence and uniqueness of solutions to a nonlocal equation with monostable nonlinearity. SIAM J. Math. Anal. 39 (2008) 1693–1709. [CrossRef] [MathSciNet] [Google Scholar]
- J. Coville, J. Dávila and S. Martínez, Pulsating fronts for nonlocal dispersion and KPP nonlinearity. Ann. Instit. H. Poincare - AN 30 (2013) 179–223. [Google Scholar]
- J. Coville and F. Hamel, On generalized principal eigenvalues of non-local operators with a drift. Nonlinear Anal. 193 (2020) 111569. [CrossRef] [MathSciNet] [Google Scholar]
- B. Cloez, B. de Saporta and T. Roget, Long-time behavior and Darwinian optimality for an asymmetric size-structured branching process. J. Math. Biol. 83 (2021). [CrossRef] [Google Scholar]
- D.J. Daley and D. Vere-Jones, An Introduction to the Theory of Point Processes: Volume II: General Theory and Structure, 2nd ed. Prob. and Its Appl., Springer (2008). [Google Scholar]
- P. Del Moral, Mean Field Simulation for Monte Carlo Integration. Chapman & Hall/CRC Monographs on Statistics & Applied Probability (2013). [CrossRef] [Google Scholar]
- P. Del Moral and L. Miclo, On the stability of nonlinear Feynman-Kac semigroups. Ann. Fac. Sci. Toulouse Math. 11 (2002) 135–175. [CrossRef] [MathSciNet] [Google Scholar]
- P. Del Moral and D. Villemonais, Exponential mixing properties for time inhomogeneous diffusion processes with killing. Bernoulli 24 (2018) 1010–1032. [CrossRef] [MathSciNet] [Google Scholar]
- C. Dellacherie and P.A. Meyer, Probabilities and Potential. North Holland (2011). [Google Scholar]
- P.A. Ferrari, H. Kesten, S. Martinez and P. Picco, Existence of quasi-stationary distributions. A renewal dynamical approach. Ann. Prob. 23 (1995) 501–521. [CrossRef] [Google Scholar]
- G. Ferré, M. Rousset and G. Stoltz, More on the long time stability of Feynman–Kac semigroups. Stoch. PDE: Anal. Comp. (2020) 1–44. [Google Scholar]
- J. Garcia-Melian and J.D. Rossi, On the principal eigenvalue of some nonlocal diffusion problems. J. Differ. Equ. 246 (2009) 21–38. [CrossRef] [Google Scholar]
- R. Hardy and S.C. Harris, A spine approach to branching diffusions with applications to Lp-convergence of martingales. Sémin. Probab. XLII. Lect. Notes Math. 1979 (2009) 281–330. [Google Scholar]
- E. Hingant and R. Yvinec, Quasi-stationary distribution and metastability for the stochastic Becker-Döring model. Electron. Commun. Prob. 26 (2021) 1–14. [CrossRef] [Google Scholar]
- L.I. Ignat, J.D. Rossi and A. San Antolin, Lower and upper bounds for the first eigenvalue of nonlocal diffusion problems in the whole space. J. Differ. Equ. 252 (2012) 6429–6447. [CrossRef] [Google Scholar]
- O. Kallenberg, Foundations of Modern Probability, 2nd edn. Springer (2002). [CrossRef] [Google Scholar]
- M. Kimura, A stochastic model concerning the maintenance of genetic variability in quantitative characters. Proc. Natl. Acad. Sci. U.S.A. 54 (1965) 731–736. [CrossRef] [PubMed] [Google Scholar]
- I. Kontoyiannis and S.P. Meyn, Spectral theory and limit theorems for geometrically ergodic Markov processes. Ann. Appl. Prob. 13 (2003) 304–362. [CrossRef] [Google Scholar]
- F. Li, J. Coville and X. Wang, On eigenvalue problems arising from nonlocal diffusion models. Discrete Contin. Dyn. Syst. 37 (2017) 879–903. [CrossRef] [MathSciNet] [Google Scholar]
- M. Mariani, E. Pardoux and A. Velleret, Metastability between the clicks of the Muller ratchet. preprint arXiv:2007.14715v2 (2022). [Google Scholar]
- S. Méléard and D. Villemonais, Quasi-stationary distributions and population processes. Prob. Surv. 9 (2012) 340–410. [Google Scholar]
- S.P. Meyn and R.L. Tweedie, Markov Chains and Stochastic Stability. Springer-Verlag, London (1993). [CrossRef] [Google Scholar]
- P. Michel, S. Mischler and B. Perthame, General relative entropy inequality: an illustration on growth models. J. Math. Pures Appl. 84 (2005) 1235–1260. [CrossRef] [MathSciNet] [Google Scholar]
- E. Pardoux, Probabilistic Models of Population Evolution : Scaling Limits, Genealogies and Interactions. Springer (2016). [CrossRef] [Google Scholar]
- P.K. Pollett, Quasi-stationary distributions: a bibliography. Available at people.smp.uq.edu.au/PhilipPollett/papers/qsds/qsds.html (2015). [Google Scholar]
- L.C.G. Rogers and D. Williams, Diffusions, Markov Processes, and Martingales, Vol. 1. Cambridge Math. Library (2000). [Google Scholar]
- M. Sharpe, General Theory of Markov Processes, Academic Press, Boston (1988). [Google Scholar]
- W. Shen and X. Xie, On principal spectrum points/principal eigenvalues of nonlocal dispersal operators and applications. Disc. Contin. Dyn. Syst. 35 (2015) 1665–1696. [CrossRef] [Google Scholar]
- D.B. Smith, A sufficient condition for the existence of a principal eigenvalue for nonlocal diffusion equations with applications. J. Math. Anal. Appl. 418 (2014) 766–774. [CrossRef] [MathSciNet] [Google Scholar]
- R.L. Tweedie, R-Theory for Markov chains on a general state space I: solidarity properties and R-recurrent chains. Ann. Prob. 2 (1974) 840–864. [Google Scholar]
- R.L. Tweedie, Quasi-stationary distributions for Markov chains on a general state space. J. Appl. Prob. 11 (1974) 726–741. [CrossRef] [Google Scholar]
- N. Torres and D. Salort, Dynamics of neural networks with elapsed time model and learning processes. Acta Appl. Math. 170 (2020) 1065–1099. [CrossRef] [MathSciNet] [Google Scholar]
- E.A. van Doorn and P.K. Pollett, Quasi-stationary distributions for discrete-state models. Eur. J. Oper. Res. 230 (2013) 1–14. [CrossRef] [Google Scholar]
- A. Velleret, Unique quasi-stationary distribution, with a possibly stabilizing extinction. Stoch. Proc. Appl. 148 (2022) 98–138. [CrossRef] [Google Scholar]
- A. Velleret, Exponential quasi-ergodicity for processes with discontinuous trajectories. second preprint version on ArXiv : arXiv:1902.01441v2 (2019). [Google Scholar]
- A. Velleret, Adaptation of a population to a changing environment under the light of quasi-stationarity. Adv. Appl. Prob. (2023) 1–52. [CrossRef] [Google Scholar]
- A. Velleret, Two level natural selection with a quasi-stationarity approach. Disc. Cont. Dyn. Syst.-B (2023) early access, doi: https://doi.org/10.3934/dcdsb.2023122. [Google Scholar]
- T. Yamada and S. Watanabe, On the uniqueness of solutions of stochastic differential equations. J. Math. Kyoto Univ. 11 (1971) 155–167. [MathSciNet] [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.