Download this PDF file Fullscreen Fullscreen Off
References
- Rami Atar and Ofer Zeitouni. Exponential stability for nonlinear filtering. Ann. Inst. H. Poincaré Probab. Statist. 33 (1997), no. 6, 697-725. Math. Reviews 1484538 (98i:60070)
- David Blackwell and Lester Dubins. Merging of opinions with increasing information. Ann. Math. Statist. 33 (1962), 882-886. Math. Reviews 0149577 (26 #7062)
- A. Budhiraja and D. Ocone. Exponential stability in discrete-time filtering for non-ergodic signals. Stochastic Process. Appl. 82 (1999), no. 2, 245-257. Math. Reviews 1700008 (2000d:94010)
- Olivier Cappé, Eric Moulines, and Tobias Rydén. Inference in hidden Markov models. Springer Series in Statistics, Springer, New York, 2005. With Randal Douc's contributions to Chapter 9 and Christian P. Robert's to Chapters 6, 7 and 13, With Chapter 14 by Gersende Fort, Philippe Soulier and Moulines, and Chapter 15 by Stéphane Boucheron and Elisabeth Gassiat. Math. Reviews 2159833 (2006e:60002)
- Pavel Chigansky and Robert Liptser. Stability of nonlinear filters in nonmixing case. Ann. Appl. Probab. 14 (2004), no. 4, 2038-2056. Math. Reviews 2099662 (2005h:62265)
- Pavel Chigansky and Robert Liptser. On a role of predictor in the filtering stability. Electron. Comm. Probab. 11 (2006), 129-140 (electronic). Math. Reviews 2240706 (2007k:60118)
- D. Crisan and K. Heine. Stability of the discrete time filter in terms of the tails of noise distributions. J. London Math. Soc. 78 (2008), 441-458.
- D. Crisan and B. Rozovsky (eds.). The Oxford University handbook of nonlinear filtering. Oxford University Press, 2009. To appear.
- Pierre Del Moral and Alice Guionnet. On the stability of interacting processes with applications to filtering and genetic algorithms. Ann. Inst. H. Poincaré Probab. Statist. 37 (2001), no. 2, 155-194. Math. Reviews 1819122 (2002k:60013)
- R. M. Dudley. Real analysis and probability. Cambridge Studies in Advanced Mathematics, vol. 74, Cambridge University Press, Cambridge, 2002. Revised reprint of the 1989 original. Math. Reviews 1932358 (2003h:60001)
- Gerald B. Folland. Real analysis, second ed. John Wiley & Sons Inc., New York, 1999. Modern techniques and their applications, A Wiley-Interscience Publication. Math. Reviews 1681462 (2000c:00001)
- Daniel Ocone and Etienne Pardoux. Asymptotic stability of the optimal filter with respect to its initial condition. SIAM J. Control Optim. 34 (1996), no. 1, 226-243. Math. Reviews 1372912 (97e:60073)
- Nadia Oudjane and Sylvain Rubenthaler. Stability and uniform particle approximation of nonlinear filters in case of non ergodic signals. Stoch. Anal. Appl. 23 (2005), no. 3, 421-448. Math. Reviews 2140972 (2005m:93153)
- A. N. Shiryaev. Probability, second ed. Graduate Texts in Mathematics, vol. 95, Springer-Verlag, New York, 1996. Translated from the first (1980) Russian edition by R. P. Boas. Math. Reviews 1368405 (97c:60003)
- R. van Handel. The stability of conditional Markov processes and Markov chains in random environments, 2008. Preprint, http://arxiv.org/abs/0801.4366
- R. van Handel. Uniform observability of hidden Markov models and filter stability for unstable signals, 2008. Preprint, http://arxiv.org/abs/0804.2885
- R. van Handel. Observability and nonlinear filtering. Probab. Th. Rel. Fields (2009). To appear. Published electronically at http://dx.doi.org/10.1007/s00440-008-0161-y

This work is licensed under a Creative Commons Attribution 3.0 License.