K. Burdzy, R. Holyst, D. Ingerman, and P. March, Configurational transition in a Fleming - Viot-type model and probabilistic interpretation of Laplacian eigenfunctions, Journal of Physics A: Mathematical and General, vol.29, issue.11
DOI : 10.1088/0305-4470/29/11/004

K. Burdzy, R. Ho?yst, and P. March, A Fleming???Viot Particle Representation??of the Dirichlet Laplacian, Communications in Mathematical Physics, vol.214, issue.3, pp.679-703, 2000.
DOI : 10.1007/s002200000294

P. Cattiaux, P. Collet, A. Lambert, S. Martinez, S. Méléard et al., Quasi-stationary distributions and diffusion models in population dynamics, The Annals of Probability, vol.37, issue.5, pp.1926-1969, 2009.
DOI : 10.1214/09-AOP451

URL : https://hal.archives-ouvertes.fr/hal-00431844

P. Cattiaux and S. Méléard, Competitive or weak cooperative stochastic Lotka???Volterra systems conditioned on non-extinction, Journal of Mathematical Biology, vol.65, issue.4, pp.797-829, 2010.
DOI : 10.1007/s00285-009-0285-4

N. Champagnat and D. Villemonais, Exponential convergence to quasi-stationary distribution and Q-process. Probability Theory and Related Fields, pp.1-41, 2015.
URL : https://hal.archives-ouvertes.fr/hal-00973509

P. and D. Moral, Mean field simulation for Monte Carlo integration, of Monographs on Statistics and Applied Probability
URL : https://hal.archives-ouvertes.fr/hal-00932211

P. , D. Moral, and A. Doucet, Particle motions in absorbing medium with hard and soft obstacles, Stochastic Anal. Appl, vol.22, issue.5, pp.1175-1207, 2004.

P. , D. Moral, and A. Guionnet, On the stability of interacting processes with applications to filtering and genetic algorithms, Ann. Inst. H. Poincaré Probab. Statist, vol.37, issue.2, pp.155-194, 2001.

P. , D. Moral, and L. Miclo, Branching and interacting particle systems approximations of Feynman-Kac formulae with applications to non-linear filtering, Séminaire de Probabilités, pp.1-145, 2000.

P. , D. Moral, and L. Miclo, A Moran particle system approximation of Feynman-Kac formulae. Stochastic Process, Appl, vol.86, issue.2, pp.193-216, 2000.

P. , D. Moral, and L. Miclo, On the stability of nonlinear Feynman-Kac semigroups

P. , D. Moral, and L. Miclo, Particle approximations of Lyapunov exponents connected to Schrödinger operators and Feynman-Kac semigroups, ESAIM Probab. Stat, vol.7, pp.171-208, 2003.

M. C. Delfour and J. Zolésio, Shapes and geometries, volume 22 of Advances in Design and Control, Metrics, analysis, differential calculus, and optimization, 2011.

S. N. Ethier and S. M. Krone, Comparing Fleming-Viot and Dawson-Watanabe processes, Stochastic Processes and their Applications, vol.60, issue.2, pp.171-190, 1995.
DOI : 10.1016/0304-4149(95)00056-9

P. A. Ferrari and N. Mari?, Quasi Stationary Distributions and Fleming-Viot Processes in Countable Spaces, Electronic Journal of Probability, vol.12, issue.0, pp.684-702, 2007.
DOI : 10.1214/EJP.v12-415

G. L. Gong, M. P. Qian, and Z. X. Zhao, Killed diffusions and their conditioning. Probab. Theory Related Fields, pp.151-167, 1988.

C. Graham and S. Méléard, Stochastic particle approximations for generalized Boltzmann models and convergence estimates, The Annals of Probability, vol.25, issue.1, pp.115-132, 1997.
DOI : 10.1214/aop/1024404281

I. Grigorescu and M. Kang, Hydrodynamic limit for a Fleming-Viot type system. Stochastic Process, Appl, vol.110, issue.1, pp.111-143, 2004.

N. Ikeda and S. Watanabe, Stochastic differential equations and diffusion processes, 1989.

R. Knobloch and L. Partzsch, Uniform conditional ergodicity and intrinsic ultracontractivity . Potential Anal, pp.107-136, 2010.

M. Kolb and A. Wübker, Spectral analysis of diffusions with jump boundary, Journal of Functional Analysis, vol.261, issue.7
DOI : 10.1016/j.jfa.2011.05.025

T. Lindvall and L. C. Rogers, Coupling of Multidimensional Diffusions by Reflection, The Annals of Probability, vol.14, issue.3, pp.860-872, 1986.
DOI : 10.1214/aop/1176992442

J. Littin and C. , Uniqueness of Quasistationary Distributions and Discrete Spectra when ??? is an Entrance Boundary and 0 is Singular, Journal of Applied Probability, vol.49, issue.03, pp.719-730, 2012.
DOI : 10.1214/09-AOP451

S. Méléard and D. Villemonais, Quasi-stationary distributions and population processes, Probability Surveys, vol.9, issue.0, pp.340-410, 2012.
DOI : 10.1214/11-PS191

Y. Miura, Ultracontractivity for Markov Semigroups and Quasi-Stationary Distributions, Stochastic Analysis and Applications, vol.50, issue.4, pp.591-601, 2014.
DOI : 10.1016/j.jfa.2007.05.003

R. G. Pinsky, On the Convergence of Diffusion Processes Conditioned to Remain in a Bounded Region for Large Time to Limiting Positive Recurrent Diffusion Processes, The Annals of Probability, vol.13, issue.2
DOI : 10.1214/aop/1176992996

E. Priola and F. Wang, Gradient estimates for diffusion semigroups with singular coefficients, Journal of Functional Analysis, vol.236, issue.1, pp.244-264, 2006.
DOI : 10.1016/j.jfa.2005.12.010

M. Rousset, On the Control of an Interacting Particle Estimation of Schr??dinger Ground States, SIAM Journal on Mathematical Analysis, vol.38, issue.3, pp.824-844, 2006.
DOI : 10.1137/050640667

E. A. Van-doorn and P. K. Pollett, Quasi-stationary distributions for discrete-state models, European Journal of Operational Research, vol.230, issue.1, pp.1-14, 2013.
DOI : 10.1016/j.ejor.2013.01.032

D. Villemonais, Interacting Particle Systems and Yaglom Limit Approximation of Diffusions with Unbounded Drift, Electronic Journal of Probability, vol.16, issue.0, pp.1663-1692, 2011.
DOI : 10.1214/EJP.v16-925

URL : https://hal.archives-ouvertes.fr/hal-00481580

D. Villemonais, Uniform tightness for time-inhomogeneous particle systems and for conditional distributions of time-inhomogeneous diffusion processes, Markov Process. Related Fields, vol.19, issue.3, pp.543-562, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00681601

D. Villemonais, General approximation method for the distribution of Markov processes conditioned not to be killed, ESAIM: Probability and Statistics, vol.18, pp.441-467, 2014.
DOI : 10.1051/ps/2013045

URL : https://hal.archives-ouvertes.fr/hal-00598085

F. Wang, Gradient estimates of Dirichlet heat semigroups and application to isoperimetric inequalities, The Annals of Probability, vol.32, issue.1A, pp.424-440, 2004.
DOI : 10.1214/aop/1078415841