Convergence of a non-failable mean-field particle system

References

• Asselah, A., Ferrari, P. A., Groisman, P., and Jonckheere, M. 2016. Fleming-Viot selects the minimal quasi-stationary distribution: The Galton-Watson case. Ann. Inst. H. Poincaré Probab. Statist. 52(2):647–668.
   Web of Science ®Google Scholar
• Bieniek, M., Burdzy, K., and Pal, S. 2012. Extinction of fleming-viot-type particle systems with strong drift. Electron. J. Probab. 17(11):1–15.
   Google Scholar
• Burdzy, K., Holyst, R., Ingerman, D., and March, P. 1996. Configurational transition in a fleming-viot-type model and probabilistic interpretation of laplacian eigenfunctions. J. Phys. A 29(29):2633–2642.
   Google Scholar
• Burdzy, K., Hołyst, R., and March, P. 2000. A Fleming-Viot particle representation of the Dirichlet Laplacian. Comm. Math. Phys. 214(3):679–703.
   Web of Science ®Google Scholar
• Champagnat, N., Coulibaly-Pasquier, A., and Villemonais, D. 2016. Exponential convergence to quasi-stationary distribution for multi-dimensional diffusion processes. arXiv:1603.07909.
   Google Scholar
• Champagnat, N., and Villemonais, D. 2015. Exponential convergence to quasi-stationary distribution for absorbed one-dimensional diffusions with killing. arXiv:1510.05794.
   Google Scholar
• Champagnat, N., and Villemonais, D. 2015. Quasi-stationary distribution for multi-dimensional birth and death processes conditioned to survival of all coordinates. arXiv:1508.03161.
   Google Scholar
• Champagnat, N., and Villemonais, D. 2015. Uniform convergence of conditional distributions for absorbed one-dimensional diffusions. arXiv:1506.02385.
   Google Scholar
• Champagnat, N., and Villemonais, D. 2016. Exponential convergence to quasi-stationary distribution and Q-process. Probab. Theory Related Fields 164(1–2):243–283.
   Web of Science ®Google Scholar
• Champagnat, N., and Villemonais, D. 2016. Uniform convergence of penalized time-inhomogeneous Markov processes. arXiv:1603.07477.
   Google Scholar
• Collet, P., Martínez, S., and San Martín, J. 2013. In Quasi-Stationary Distributions. Markov chains, diffusions and dynamical systems. ( Probability and its Applications). Heidelberg: Springer.
   Google Scholar
• Dautray, R., and Lions, J.-L. 1993. Mathematical Analysis and Numerical Methods for Science and Technology, Vol. 6. Berlin: Springer-Verlag.
   Google Scholar
• Del Moral, P. Feynman-Kac models and interacting particle systems. http://people.bordeaux.inria.fr/pierre.delmoral/simulinks.html
   Google Scholar
• Del Moral, P. 1998. Measure-valued processes and interacting particle systems. Application to nonlinear filtering problems. Ann. Appl. Probab. 8(2):438–495.
   Web of Science ®Google Scholar
• Del Moral, P., and Miclo, L. 2003. Particle approximations of Lyapunov exponents connected to Schrödinger operators and Feynman-Kac semigroups. ESAIM Probab. Stat. 7:171–208.
   Google Scholar
• Ferrari, P. A., and Marić, N. 2007. Quasi stationary distributions and Fleming-Viot processes in countable spaces. Electron. J. Probab. 12(24):684–702. [ online]
   Google Scholar
• Grigorescu, I., and Kang, M. 2004. Hydrodynamic limit for a Fleming-Viot type system. Stochastic Process. Appl. 110(1):111–143.
   Web of Science ®Google Scholar
• Méléard, S., and Villemonais, D. 2012. Quasi-stationary distributions and population processes. Probab. Surv. 9:340–410.
   Google Scholar
• Meyn, S., and Tweedie, R. 2009. Markov Chains and Stochastic Stability. New York: Cambridge University Press.
   Google Scholar
• Rousset, M. 2006. On the control of an interacting particle estimation of Schrödinger ground states. SIAM J. Math. Anal. 38(3):824–844. [ online]
   Web of Science ®Google Scholar
• van Doorn, E. A., and Pollett, P. K. 2013. Quasi-stationary distributions for discrete-state models. European J. Oper. Res. 230(1):1–14.
   Web of Science ®Google Scholar
• Villemonais, D. 2011. Interacting particle systems and Yaglom limit approximation of diffusions with unbounded drift. Electron. J. Probab. 16(61):1663–1692.
   Google Scholar
• Villemonais, D. 2014. General approximation method for the distribution of markov processes conditioned not to be killed. ESAIM: Probability and Statistics [ eFirst]
   PubMed Web of Science ®Google Scholar
• Villemonais, D. 2015. Minimal quasi-stationary distribution approximation for a birth and death process. Electron. J. Probab. 20(30):1–18.
   Google Scholar
• Zoia, A., Dumonteil, E., and Mazzolo, A. 2011. Collision densities and mean residence times for d-dimensional exponential flights. Phys. Rev. E 83:041137.
   Web of Science ®Google Scholar