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

 Access to full text

 Full (PDF)

1. [1] R. Atar, Exponential stability for nonlinear filtering of diffusion processes in non-compact domain, Ann. Probab.26 (1998) 1552-1574. Zbl0930.93080MR1675039
2. [2] R. Atar, O. Zeitouni, Exponential stability for nonlinear filtering, Annales de l'Institut H. Poincaré Probabilites et Statistique33 (1997) 697-725. Zbl0888.93057MR1484538
3. [3] R. Atar, O. Zeitouni, Lyapunov exponents for finite state nonlinear filtering, SIAM J. Control Optim.35 (1997) 36-55. Zbl0940.93073MR1430282
4. [4] A. Bhatt, A. Budhiraja, R. Karandikar, Markov property and ergodicity of the nonlinear filter, SIAM J. Control Optim.39 (2000) 928-949. Zbl0970.60047MR1786337
5. [5] A. Bhatt, G. Kallianpur, R. Karandikar, Robustness of the nonlinear filter, Stochastic Process. Appl.81 (1999) 247-254. Zbl0963.60039MR1694557
6. [6] A. Budhiraja, Ergodic properties of the nonlinear filter, Stochastic Process. Appl.95 (2001) 1-24. Zbl1059.60054MR1847089
7. [7] A. Budhiraja, H.J. Kushner, Approximation and limit results for nonlinear filters over an infinite time interval, SIAM J. Control Optim.37 (1997) 1946-1979. Zbl0934.93064MR1720146
8. [8] A. Budhiraja, H.J. Kushner, Robustness of nonlinear filters over the infinite time interval, SIAM J. Control Optim.36 (1998) 1618-1637. Zbl0915.93063MR1626884
9. [9] A. Budhiraja, H.J. Kushner, 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. Zbl1031.93148MR1776660
10. [10] A. Budhiraja, H.J. Kushner, Monte Carlo algorithms and asymptotic problems in nonlinear filtering, in: Stochastics in Finite/Infinite Dimensions, Trends Math., Birkhäuser, Boston, 2001, pp. 59-87. Zbl1129.93535MR1797081
11. [11] A. Budhiraja, D. Ocone, Exponential stability of discrete time filters without signal ergodicity, System Control Lett.30 (1997) 185-193. Zbl0901.93066MR1455877
12. [12] A. Budhiraja, D. Ocone, Exponential stability in discrete time filtering for non-ergodic signals, Stochastic Process. Appl.82 (1999) 245-257. Zbl1056.93065MR1700008
13. [13] P. Chigansky, R. Liptser, Private communication. 
14. [14] P. Chigansky, P. Baxendale, R. Liptser, Asymptotic stability of the Wonham filter. Ergodic and nonergodic signals, Preprint in Arxiv. Zbl1101.93074MR2086177
15. [15] F. Cérou, Long time asymptotics for some dynamical noise free non linear filtering problems, Rapport de Recherche 2446, INRIA, December, 1994. Zbl0842.93069
16. [16] J.M.C. Clark, D.L. Ocone, C. Coumarbatch, Relative entropy and error bounds for filtering of Markov processes, Math. Control Signals Syst.12 (1999) 346-360. Zbl0940.93072MR1728373
17. [17] G. Da Prato, M. Fuhrman, P. Malliavin, Asymptotic ergodicity for the Zakai filtering equation, C. R. Acad. Sci. Paris Serie I321 (1995) 613-616. Zbl0838.60039MR1356563
18. [18] P. Del Moral, A. Guionnet, On the stability of measure valued processes with applications to filtering, C. R. Acad. Sci. Paris Serie I329 (1999) 429-434. Zbl0935.92001MR1710091
19. [19] B. Delyon, O. Zeitouni, Lyapunov exponents for filtering problems, in: Applied Stochastic Analysis (London, 1989), Stochastics Monogr., 5, Gordon and Breach, New York, 1991, pp. 511-521. Zbl0738.60033MR1108433
20. [20] G. Kallianpur, Stochastic Filtering Theory, Springer-Verlag, New York, 1980. Zbl0458.60001MR583435
21. [21] R.L. Karandikar, On pathwise stochastic integration, Stochastic Process. Appl.57 (1995) 11-18. Zbl0816.60047MR1327950
22. [22] H. Kunita, Asymptotic behavior of the nonlinear filtering errors of Markov processes, J. Multivariate Anal.1 (1971) 365-393. Zbl0245.93027MR301812
23. [23] H. Kunita, Ergodic properties of nonlinear filtering processes, in: Alexander K.C., Watkins J.C. (Eds.), Spatial Stochastic Processes, 1991. Zbl0742.60062MR1144099
24. [24] F. Le Gland, L. Mevel, Exponential forgetting and geometric ergodicity in hidden Markov models, Math. Control Signals Syst.13 (2000) 63-93. Zbl0941.93053MR1742140
25. [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. Zbl1060.93094MR1989630
26. [26] D. Ocone, Asymptotic stability of Benes filters, Stochastic Anal. Appl.17 (1999) 1053-1074. Zbl0945.60032MR1721933
27. [27] D. Ocone, 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. Zbl0920.93036MR1702976
28. [28] D. Ocone, E. Pardoux, Asymptotic stability of the optimal filter with respect to its initial condition, SIAM J. Control Optim.34 (1996) 226-243. Zbl1035.93508MR1372912
29. [29] L. Stettner, 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, pp. 279-292. Zbl0683.93082MR1236074
30. [30] L. Stettner, Invariant measures of pair: State, approximate filtering process, Colloq. Math.LXII (1991) 347-352. Zbl0795.60028MR1142935
31. [31] H. Totoki, A class of special flows, Z. Wahr. Verw. Geb.15 (1970) 157-167. Zbl0193.45903MR279279
32. [32] H.V. Weizsäcker, Exchanging the order of taking suprema and countable intersections of σ algebras, Ann. Inst. Henri Poincaré B19 (1) (1983) 91-100. Zbl0509.60002
33. [33] D. Williams, Probability with Martingales, Cambridge University Press, 1991. Zbl0722.60001MR1155402