A. Asselah, P. A. Ferrari, and P. Groisman, Quasistationary Distributions and Fleming-Viot Processes in Finite Spaces, Journal of Applied Probability, vol.11, issue.02, pp.322-332, 2011.
DOI : 10.1016/j.spa.2003.10.010

URL : https://hal.archives-ouvertes.fr/hal-00692986

G. I. Bell, Models of carcinogenesis as an escape from mitotic inhibitors, Science, vol.192, issue.4239, pp.569-572, 1976.
DOI : 10.1126/science.130679

W. A. Beyer and M. S. Waterman, A conditioned random walk with applications, Los Alamos Scientific Laboratory, 1977.

W. Böhm and M. S. , Gopal On Random Walks with Barriers and their Application to Queues. Forschungsberichte / Institut für Statistik, 21, 1991.

H. P. Chan, P. Del-moral, and A. Jasra, A Sharp First Order Analysis of Feynman-Kac Particle Models Part II, 2016.

F. Cerou, P. Del-moral, and &. A. Guyader, A non-asymptotic theorem for unnormalized Feynman-Kac particle models, pp.629-649, 2011.
URL : https://hal.archives-ouvertes.fr/inria-00337392

Y. Chen, P. Diaconis, S. Holmes, and &. J. Liu, Sequential Monte Carlo Methods for Statistical Analysis of Tables, Journal of the American Statistical Association, vol.100, issue.469, pp.109-120, 2005.
DOI : 10.1198/016214504000001303

N. Chopin, Central limit theorem for sequential Monte Carlo methods and its application to Bayesian inference, The Annals of Statistics, vol.32, issue.6, pp.2385-2411, 2004.
DOI : 10.1214/009053604000000698

URL : http://doi.org/10.1214/009053604000000698

P. and D. Moral, Feynman-Kac Formulae: Genealogical and Interacting Particle Systems with Applications, 2004.

P. and D. Moral, Mean Field Simulation for Monte Carlo Integration, 2013.
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 Analysis and Applications, pp.1175-1207, 2004.

P. , D. Moral, and A. Guionnet, On the stability of Measure Valued Processes with Applications to filtering, C.R. Acad. Sci. Paris, t, vol.329, pp.429-434, 1999.

P. , D. Moral, and A. Guionnet, On the stability of interacting processes with applications to filtering and genetic algorithms, Annales de l'Institut Henri Poincar¨?¿Poincar¨?¿ 1 2, pp.155-194, 2001.

P. Del-moral and J. Jacod, Interacting particle filtering with discrete-time observations: asymptotic behaviour in the Gaussian case Stochastics in finite/infinite dimensions, pp.101-123, 2001.

P. , D. Moral, and L. Miclo, Branching and Interacting Particle Systems Approximations of Feynman-Kac Formulae with Applications to Non-Linear Filtering, Lecture Notes in Mathematics, vol.1729, pp.1-145, 2000.

P. , D. Moral, and L. Miclo, On the Stability of Non Linear Semigroup of Feynman-Kac Type, Annales de la Faculté des Sciences de Toulouse, 2002.

P. , D. Moral, and D. , Villemonais Exponential mixing properties for time inhomogeneous diffusion processes with killing arXiv:1412.2627, 2014.

P. Diaconis and D. Stroock, Geometric Bounds for Eigenvalues of Markov Chains, The Annals of Applied Probability, vol.1, issue.1, pp.36-61, 1991.
DOI : 10.1214/aoap/1177005980

P. Diaconis and L. Miclo, On quantitative convergence to quasi-stationarity. ArXiv:1406, p.1805, 2014.
DOI : 10.5802/afst.1472

URL : https://hal.archives-ouvertes.fr/hal-01002622

A. M. El-shehawey and ;. B. , On a gambler's ruin problem, Mathematica Slovaca, vol.47, issue.4, pp.483-488, 1997.

C. J. Everett and P. R. Stein, The combinatorics of random walk with absorbing barriers, Discrete Mathematics, vol.17, issue.1, pp.27-45, 1977.
DOI : 10.1016/0012-365X(77)90019-X

W. Feller, An Introduction to Probability Theory and its Applications, 1968.

P. A. Ferrari and S. , Existence of non-trivial quasi-stationary distributions in the birth-death chain, Advances in Applied Probability, vol.56, issue.04, pp.795-813, 1992.
DOI : 10.2307/3214486

M. B. Giles, Multilevel Monte Carlo methods, Acta Numerica, vol.24, pp.259-328, 2015.
DOI : 10.1017/S096249291500001X

H. C. Gupta and A. Seth, Random walk in the presence of absorbing barriers, Proc. Nat. Inst. Sci. India. A, vol.32, pp.472-480, 1966.

M. Kac, Random Walk in the Presence of Absorbing Barriers, The Annals of Mathematical Statistics, vol.16, issue.1, pp.62-67, 1945.
DOI : 10.1214/aoms/1177731171

G. Kreweras, Sur leséventailsleséventails de segments, pp.3-41, 1970.

N. Maric, Fleming-Viot particle system driven by a random walk on N. Arxiv 1405, Journal of Stat. Phys, vol.0094, issue.160, p.548, 2014.

D. S. Novikov, E. Fieremans, J. H. Jensen, and J. A. Helpern, Random walks with barriers, Nature Physics, vol.303, issue.6, pp.508-514, 2011.
DOI : 10.1002/nbm.1577

URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3114643

E. Seneta, QUASI-STATIONARY BEHAVIOUR IN THE RANDOM WALK WITH CONTINUOUS TIME, Australian Journal of Statistics, vol.85, issue.2, pp.92-98, 1966.
DOI : 10.2140/pjm.1958.8.87

F. Stern, Absorption sequences, Fibonacci Quarterly, vol.17, pp.275-280, 1979.

A. M. Yaglom, Certain limit theorems of the theory of branching stochastic processes (in Russian), Dokl. Akad. Nauk SSSR, vol.56, pp.795-798, 1947.

J. Wang and J. A. Jasra, Monte Carlo algorithms for computing $$\alpha $$ ?? -permanents, Statistics and Computing, vol.21, issue.1-2, pp.231-248, 2016.
DOI : 10.1089/cmb.2013.0082

N. Whiteley, Stability properties of some particle filters, The Annals of Applied Probability, vol.23, issue.6, pp.2500-2537, 2013.
DOI : 10.1214/12-AAP909

URL : http://doi.org/10.1214/12-aap909

N. A. Whiteley and . Lee, Twisted particle filters, The Annals of Statistics, vol.42, issue.1, pp.115-141, 2014.
DOI : 10.1214/13-AOS1167SUPP

URL : http://doi.org/10.1214/13-aos1167