. Springer-verlag, Die Grundlehren der mathematischen Wissenschaften, Band 196, 1972.

R. Atar and O. Zeitouni, Exponential stability for nonlinear ltering, Ann. Inst. H. Poincaré Probab. Statist, vol.33, issue.6, p.697725, 1997.

J. Bertoin, Random fragmentation and coagulation processes, volume 102 de Cambridge Studies in Advanced Mathematics, 2006.

A. Budhiraja and D. Ocone, Exponential stability in discrete-time ltering for non-ergodic signals [Bon82] Lennart Bondesson : On simulation from innitely divisible distributions, Bud03] A. Budhiraja : Asymptotic stability, ergodicity and other asymptotic properties of the nonlinear lter. Ann. Inst. H. Poincaré Probab. Statist, p.245257855869919941, 1982.

M. Chaleyat-maurel and V. Genon-catalot, Computable innite-dimensional lters with applications to discretized diusion processes. Stochastic Process Heine : Stability of the discrete time lter in terms of the tails of noise distributions, Appl. J. Lond. Math. Soc, vol.116, issue.1022, pp.14471467-78441458, 2006.

R. Chen-et-jun and S. Liu, Mixture Kalman lters, J. R. Stat. Soc. Ser. B Stat. Methodol, vol.62, issue.3, p.493508, 2000.

P. Del and M. , Feynman-Kac formulae. Probability and its Applications, Genealogical and interacting particle systems with applications, 2004.
URL : https://hal.archives-ouvertes.fr/inria-00410165

R. Douc, G. Fort, E. Moulines, and P. Priouret, Forgetting the initial distribution for Hidden Markov Models, Stochastic Processes and their Applications, vol.119, issue.4, p.12351256, 2009.
DOI : 10.1016/j.spa.2008.05.007
URL : https://hal.archives-ouvertes.fr/hal-00392629

P. Del, M. , and A. Guionnet, On the stability of interacting processes with applications to ltering and genetic algorithms, Ann. Inst. H. Poincaré Probab. Statist, vol.37, issue.2, p.155194, 2001.

A. Doucet, S. Godsill, and C. , Andrieu : On sequential monte-carlo methods for bayesian ltering [dlPG99] Víctor H. de la Peña et Evarist Giné : Decoupling. Probability and its Applications From dependence to independence, Randomly stopped processes. U -statistics and processes. Martingales and beyond, DM83] E. B. Dynkin et A. Mandelbaum : Symmetric statistics, Poisson point processes, and multiple Wiener integrals, p.739745, 1983.

P. Del, M. , and L. Miclo, Branching and interacting particle systems approximations of Feynman-Kac formulae with applications to non-linear ltering [Dur02] Rick Durrett : Probability models for DNA sequence evolution, Séminaire de Probabilités Probability and its Applications, p.1145, 2000.

J. Warren and . Ewens, Mathematical population genetics. I, volume 27 de Interdisciplinary Applied Mathematics Theoretical introduction. [Fou] Nicolas Fournier : Simulation and approximation of lévy-driven stochastic dierential equations, 2004.

C. Graham and S. Méléard, Chaos hypothesis for a system interacting through shared resources. Probab. Theory Related Fields, p.157173, 1994.

C. Graham and S. Méléard, Stochastic particle approximations for generalized Boltzmann models and convergence estimates, The Annals of Probability, vol.25, issue.1, p.115132, 1997.
DOI : 10.1214/aop/1024404281

C. Graham and S. Méléard, Probabilistic tools and Monte-Carlo approximations for some Boltzmann equations, CEMRACS 1999 (Orsay), volume 10 de ESAIM Proc, p.77126
DOI : 10.1051/proc:2001010

K. Heine and D. Crisan, Uniform approximations of discretetime lters Statistical analysis of selfsimilar conservative fragmentation chains, Adv. in Appl. Probab, vol.40, issue.4, p.9791001, 2008.

J. [. Jakubowski, G. Mémin, . G. Pagès-[-ko88-]-t, D. L. Kurtz, and . Ocone, Convergence en loi des suites d'intégrales stochastiques sur l'espace D 1 de Skorokhod. Probab . Theory Related Fields Unique characterization of conditional distributions in nonlinear ltering, p.11113780107, 1988.

G. Thomas, P. Kurtz, and . Protter, Characterizing the weak convergence of stochastic integrals, In Stochastic analysis, vol.167, p.255259, 1990.

G. Thomas, P. Kurtz, and . Protter, Weak limit theorems for stochastic integrals and stochastic dierential equations, Ann. Probab, vol.19, issue.3, p.10351070, 1991.

G. Thomas, P. Kurtz, and . Protter, Wong-Zakai corrections, random evolutions, and simulation schemes for SDEs, Stochastic analysis, p.331346, 1991.

M. L. Kleptsyna, A. J. Yulee90-]-a, and . Lee, Veretennikov : On discrete time ergodic lters with wrong initial data. Probab. Theory Related Fields Theory and practice. [LO03] François LeGland et Nadia Oudjane : A robustication approach to stability and to uniform particle approximation of nonlinear lters : the example of pseudo-mixing signals, Hiroshi Kunita : Asymptotic behavior of the nonlinear ltering errors of Markov processes François Le Gland et Nadia Oudjane : Stability and uniform approximation of nonlinear lters using the Hilbert metric and application to particle lters, pp.3653933-4411444279316144187, 1971.

S. Méléard, Convergence of the uctuations for interacting diusions with jumps associated with Boltzmann equations, Stochastics Stochastics Rep, vol.63, issue.3-4, p.195225, 1998.

J. Mémin and L. Sªomi«ski, Condition UT et stabilité en loi des solutions d'équations diérentielles stochastiques, Séminaire de Probabilités, XXV, volume 1485 de Lecture Notes in MathMT09] Sean Meyn et Richard L. Tweedie : Markov chains and stochastic stability, p.162177, 1991.

G. Rota and T. C. Wallstrom, Stochastic integrals : a combinatorial approach Simon Tavaré : Ancestral inference in population genetics In Lectures on probability theory and statistics, volume 1837 de Lecture Notes in Math [vH08] Ramon van Handel : Discrete time nonlinear lters with informative observations are stable, Observability and nonlinear ltering. Probab. Theory Related Fields Handel : Uniform time average consistency of Monte Carlo particle lters. Stochastic Process, pp.12571283-1188562, 1997.