Asymptotic stability, ergodicity and other asymptotic properties of the nonlinear filter

Annales de l'institut Henri Poincare (B) Probability and Statistics

Volumn 39, Issue 6, 2003, Pages 919-941

  Budhiraja, A ^a  

^a University of North Carolina at Chapel Hill   (United States)

Author keywords

Asymptotic stability; Invariant measures; Measure valued processes; Nonlinear filtering

Indexed keywords

EID: 0141648366     PISSN: 02460203     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0246-0203(03)00022-0     Document Type: Article

References (33)

1. Atar R. Exponential stability for nonlinear filtering of diffusion processes in non-compact domain Ann. Probab. 26 1998 1552-1574
2. Atar R. Zeitouni O. Exponential stability for nonlinear filtering Annales de l'Institut H. Poincaré Probabilites et Statistique 33 1997 697-725
3. Atar R. Zeitouni O. Lyapunov exponents for finite state nonlinear filtering SIAM J. Control Optim. 35 1997 36-55
4. Bhatt A. Budhiraja A. Karandikar R. Markov property and ergodicity of the nonlinear filter SIAM J. Control Optim. 39 2000 928-949
5. Bhatt A. Kallianpur G. Karandikar R. Robustness of the nonlinear filter Stochastic Process. Appl. 81 1999 247-254
6. Budhiraja A. Ergodic properties of the nonlinear filter Stochastic Process. Appl. 95 2001 1-24
7. Budhiraja A. Kushner H.J. Approximation and limit results for nonlinear filters over an infinite time interval SIAM J. Control Optim. 37 1997 1946-1979
8. Budhiraja A. Kushner H.J. Robustness of nonlinear filters over the infinite time interval SIAM J. Control Optim. 36 1998 1618-1637
9. Budhiraja A. Kushner H.J. Approximation and limit results for nonlinear filters over an infinite time interval: Part II, random sampling algorithms SIAM J. Control Optim. 38 2000 1874-1908
10. Budhiraja A. Kushner H.J. Monte Carlo algorithms and asymptotic problems in nonlinear filtering Stochastics in Finite/Infinite Dimensions Trends Math. 2001 59-87 Birkhäuser Boston
11. Budhiraja A. Ocone D. Exponential stability of discrete time filters without signal ergodicity System Control Lett. 30 1997 185-193
12. Budhiraja A. Ocone D. Exponential stability in discrete time filtering for non-ergodic signals Stochastic Process. Appl. 82 1999 245-257
13. P. Chigansky, R. Liptser, Private communication
14. P. Chigansky, P. Baxendale, R. Liptser, Asymptotic stability of the Wonham filter. Ergodic and nonergodic signals, Preprint in Arxiv
15. F. Cérou, Long time asymptotics for some dynamical noise free non linear filtering problems, Rapport de Recherche 2446, INRIA, December, 1994
16. Clark J.M.C. Ocone D.L. Coumarbatch C. Relative entropy and error bounds for filtering of Markov processes Math. Control Signals Syst. 12 1999 346-360
17. Da Prato G. Fuhrman M. Malliavin P. Asymptotic ergodicity for the Zakai filtering equation C. R. Acad. Sci. Paris Serie I 321 1995 613-616
18. Del Moral P. Guionnet A. On the stability of measure valued processes with applications to filtering C. R. Acad. Sci. Paris Serie I 329 1999 429-434
19. Delyon B. Zeitouni O. Lyapunov exponents for filtering problems Applied Stochastic Analysis (London, 1989) Stochastics Monogr. 5 1991 511-521 Gordon and Breach New York
20. Kallianpur G. Stochastic Filtering Theory 1980 Springer-Verlag New York
21. Karandikar R.L. On pathwise stochastic integration Stochastic Process. Appl. 57 1995 11-18
22. Kunita H. Asymptotic behavior of the nonlinear filtering errors of Markov processes J. Multivariate Anal. 1 1971 365-393
23. Kunita H. Ergodic properties of nonlinear filtering processes, in: Alexander K.C. Watkins J.C. (Eds.), Spatial Stochastic Processes 1991
24. Le Gland F. Mevel L. Exponential forgetting and geometric ergodicity in hidden Markov models Math. Control Signals Syst. 13 2000 63-93
25. F. Le Gland, N. Oudjane, A robustification approach to stability and to uniform particle approximation of nonlinear filters: the example of pseudo-mixing signals, Preprint
26. Ocone D. Asymptotic stability of Benes filters Stochastic Anal. Appl. 17 1999 1053-1074
27. Ocone D. Entropy inequalities and entropy dynamics in nonlinear filtering of diffusion processes, in: McEneaney W. Yin G. Zhang Q. (Eds.), Stochastic Analysis, Control, Optimization and Applications 1999
28. Ocone D. Pardoux E. Asymptotic stability of the optimal filter with respect to its initial condition SIAM J. Control Optim. 34 1996 226-243
29. Stettner L. On invariant measures of filtering processes, in: Helmes K. Christopeit N. Kohlmann M. (Eds.), Stochastic Differential Systems, Proc. 4th Bad Honnef Conf., 1988 Lecture Notes in Control and Inform Sci. 1989 279-292
30. Stettner L. Invariant measures of pair: State, approximate filtering process Colloq. Math. LXII 1991 347-352
31. Totoki H. A class of special flows Z. Wahr. Verw. Geb. 15 1970 157-167
32. Weizsäcker H.V. Exchanging the order of taking suprema and countable intersections of σ algebras Ann. Inst. Henri Poincaré B 19 1 1983 91-100
33. Williams D. Probability with Martingales 1991 Cambridge University Press