Stability and uniform approximation of nonlinear filters using the Hilbert metric and application to particle filters
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Del Moral, P. and Guionnet, A. (2001). On the stability of interacting processes with applications to filtering and genetic algorithms. <i>Ann. Inst. H. Poincaré Probab. Statist.</i> <b>37</b> 155--194.
Le Gland, F. and Mevel, L. (2000). Exponential forgetting and geometric ergodicity in hidden Markov models. <i>Math. Control Signals Systems</i> <b>13</b> 63--93.
Atar, R., Viens, F. and Zeitouni, O. (1999). Robustness of Zakai's equation via Feynman--Kac representations. In <i>Stochastic Analysis</i>,<i> Control</i>,<i> Optimization and Applications</i>:<i> A Volume in Honor of Wendell H. Fleming</i> (W. M. McEneaney, G. G. Yin and Q. Zhang, eds.) 339--352. Birkhäuser, Boston.
Birkhoff, G. (1967). <i>Lattice Theory</i>, <i>Colloquium Publications</i>, 3rd ed. Amer. Math. Soc., Providence, RI.
Devroye, L. (1987). <i>A Course on Density Estimation</i>. Birkhäuser, Boston.
Doucet, A., de Freitas, N. and Gordon, N., eds. (2001). <i>Sequential Monte Carlo Methods in Practice</i>. Springer, New York.
Le Gland, F., Musso, C. and Oudjane, N. (1998). An analysis of regularized interacting particle methods for nonlinear filtering. In <i>Preprints of the Third IEEE European Workshop on Computer---Intensive Methods in Control and Data Processing</i>,<i> Prague 1998</i> (J. Rojíček, M. Valečkova, M. Kárný and K. Warwick, eds.) 167--174.
Musso, C. and Oudjane, N. (1998). Regularization schemes for branching particle systems as a numerical solving method of the nonlinear filtering problem. In <i>Proceedings of the Irish Signals and Systems Conference</i>,<i> Dublin 1998</i>.
Musso, C., Oudjane, N. and Le Gland, F. (2001). Improving regularized particle filters. In <i>Sequential Monte Carlo Methods in Practice</i> (A. Doucet, N. de Freitas and N. Gordon, eds.) 247--271. Springer, New York.
Neveu, J. (1975). <i>Discrete-Parameter Martingales</i>. North-Holland, Amsterdam.
Oudjane, N. and Musso, C. (1999). Multiple model particle filter. In <i>17ème Colloque GRETSI</i>,<i> Vannes 1999</i> 681--684.
Oudjane, N. and Rubenthaler, S. (2003). Stability and uniform particle approximation of nonlinear filters in case of nonergodic signal. Prépublication PMA--786, Laboratoire de Probabilités et Modèles Aléatoires, Univ. Paris VI. Available at www.proba.jussieu.fr/mathdoc/textes/PMA-786.pdf.
Silverman, B. W. (1986). <i>Density Estimation for Statistics and Data Analysis</i>. Chapman and Hall, London.
Atar, R. and Zeitouni, O. (1997). Lyapunov exponents for finite state nonlinear filtering. <i>SIAM J. Control Optim.</i> <b>35</b> 36--55.
Atar, R. (1998). Exponential stability for nonlinear filtering of diffusion processes in a noncompact domain. <i>Ann. Probab.</i> <b>26</b> 1552--1574.
Atar, R. and Zeitouni, O. (1997). Exponential stability for nonlinear filtering. <i>Ann. Inst. H. Poincaré Probab. Statist.</i> <b>33</b> 697--725.
Budhiraja, A. S. and Ocone, D. L. (1997). Exponential stability of discrete-time filters for bounded observation noise. <i>Systems Control Lett.</i> <b>30</b> 185--193.
Budhiraja, A. S. and Ocone, D. L. (1999). Exponential stability in discrete-time filtering for nonergodic signals. <i>Stochastic Process. Appl.</i> <b>82</b> 245--257.
Da Prato, G., Fuhrman, M. and Malliavin, P. (1999). Asymptotic ergodicity of the process of conditional law in some problem of nonlinear filtering. <i>J. Funct. Anal.</i> <b>164</b> 356--377.
Del Moral, P., Jacod, J. and Protter, P. (2001). The Monte Carlo method for filtering with discrete-time observations. <i>Probab. Theory Related Fields</i> <b>120</b> 346--368.
Del Moral, P. and Miclo, L. (2000). Branching and interacting particle systems approximations of Feynman--Kac formulae with applications to nonlinear filtering. <i>Séminaire de Probabilités XXXIV</i>. <i>Lecture Notes in Math.</i> <b>1729</b> 1--145. Springer, Berlin.
Gordon, N. J., Salmond, D. J. and Smith, A. F. M. (1993). Novel approach to nonlinear/non-Gaussian Bayesian state estimation. <i>IEE Proc. on Radar and Signal Processing</i> <b>140</b> 107--113.
Holmström, L. and Klemelä, J. (1992). Asymptotic bounds for the expected $L_1$ error of a multivariate kernel density estimator. <i>J. Multivariate Anal.</i> <b>42</b> 245--266.
Hopf, E. (1963). An inequality for positive integral linear operators. <i>J. Math. Mechanics</i> <b>12</b> 683--692.
Hürzeler, M. and Künsch, H. R. (1998). Monte Carlo approximations for general state space models. <i>J. Comput. Graph. Statist.</i> <b>7</b> 175--193.
Le Gland, F. and Mevel, L. (2000). Basic properties of the projective product, with application to products of column-allowable nonnegative matrices. <i>Math. Control Signals Systems</i> <b>13</b> 41--62.
Le Gland, F. and Oudjane, N. (2003). A robustification approach to stability and to uniform particle approximation of nonlinear filters: The example of pseudo mixing signals. <i>Stochastic Process. Appl.</i> <b>106</b> 279--316.
Ocone, D. L. and Pardoux, E. (1996). Asymptotic stability of the optimal filter with respect to its initial condition. <i>SIAM J. Control Optim.</i> <b>34</b> 226--243.