no. 6
Asymptotic stability, ergodicity and other asymptotic properties of the nonlinear filter
Annales de l'I.H.P. Probabilités et statistiques, Tome 39 (2003) no. 6, pp. 919-941. 
@article{AIHPB_2003__39_6_919_0,
     author = {Budhiraja, A.},
     title = {Asymptotic stability, ergodicity and other asymptotic properties of the nonlinear filter},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {919--941},
     publisher = {Elsevier},
     volume = {39},
     number = {6},
     year = {2003},
     doi = {10.1016/S0246-0203(03)00022-0},
     mrnumber = {2010391},
     zbl = {02003841},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/S0246-0203(03)00022-0/}
}
TY  - JOUR
AU  - Budhiraja, A.
TI  - Asymptotic stability, ergodicity and other asymptotic properties of the nonlinear filter
JO  - Annales de l'I.H.P. Probabilités et statistiques
PY  - 2003
SP  - 919
EP  - 941
VL  - 39
IS  - 6
PB  - Elsevier
UR  - http://archive.numdam.org/articles/10.1016/S0246-0203(03)00022-0/
DO  - 10.1016/S0246-0203(03)00022-0
LA  - en
ID  - AIHPB_2003__39_6_919_0
ER  - 
%0 Journal Article
%A Budhiraja, A.
%T Asymptotic stability, ergodicity and other asymptotic properties of the nonlinear filter
%J Annales de l'I.H.P. Probabilités et statistiques
%D 2003
%P 919-941
%V 39
%N 6
%I Elsevier
%U http://archive.numdam.org/articles/10.1016/S0246-0203(03)00022-0/
%R 10.1016/S0246-0203(03)00022-0
%G en
%F AIHPB_2003__39_6_919_0
Budhiraja, A. Asymptotic stability, ergodicity and other asymptotic properties of the nonlinear filter. Annales de l'I.H.P. Probabilités et statistiques, Tome 39 (2003) no. 6, pp. 919-941. doi : 10.1016/S0246-0203(03)00022-0. http://archive.numdam.org/articles/10.1016/S0246-0203(03)00022-0/

[1] R. Atar, Exponential stability for nonlinear filtering of diffusion processes in non-compact domain, Ann. Probab. 26 (1998) 1552-1574. | MR | Zbl

[2] R. Atar, O. Zeitouni, Exponential stability for nonlinear filtering, Annales de l'Institut H. Poincaré Probabilites et Statistique 33 (1997) 697-725. | Numdam | MR | Zbl

[3] R. Atar, O. Zeitouni, Lyapunov exponents for finite state nonlinear filtering, SIAM J. Control Optim. 35 (1997) 36-55. | MR | Zbl

[4] A. Bhatt, A. Budhiraja, R. Karandikar, Markov property and ergodicity of the nonlinear filter, SIAM J. Control Optim. 39 (2000) 928-949. | MR | Zbl

[5] A. Bhatt, G. Kallianpur, R. Karandikar, Robustness of the nonlinear filter, Stochastic Process. Appl. 81 (1999) 247-254. | MR | Zbl

[6] A. Budhiraja, Ergodic properties of the nonlinear filter, Stochastic Process. Appl. 95 (2001) 1-24. | MR | Zbl

[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. | MR | Zbl

[8] A. Budhiraja, H.J. Kushner, Robustness of nonlinear filters over the infinite time interval, SIAM J. Control Optim. 36 (1998) 1618-1637. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[11] A. Budhiraja, D. Ocone, Exponential stability of discrete time filters without signal ergodicity, System Control Lett. 30 (1997) 185-193. | MR | Zbl

[12] A. Budhiraja, D. Ocone, Exponential stability in discrete time filtering for non-ergodic signals, Stochastic Process. Appl. 82 (1999) 245-257. | MR | Zbl

[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. | MR

[15] F. Cérou, Long time asymptotics for some dynamical noise free non linear filtering problems, Rapport de Recherche 2446, INRIA, December, 1994.

[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. | MR | Zbl

[17] G. Da Prato, M. Fuhrman, P. Malliavin, Asymptotic ergodicity for the Zakai filtering equation, C. R. Acad. Sci. Paris Serie I 321 (1995) 613-616. | MR | Zbl

[18] P. Del Moral, A. Guionnet, On the stability of measure valued processes with applications to filtering, C. R. Acad. Sci. Paris Serie I 329 (1999) 429-434. | MR | Zbl

[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. | MR | Zbl

[20] G. Kallianpur, Stochastic Filtering Theory, Springer-Verlag, New York, 1980. | MR | Zbl

[21] R.L. Karandikar, On pathwise stochastic integration, Stochastic Process. Appl. 57 (1995) 11-18. | MR | Zbl

[22] H. Kunita, Asymptotic behavior of the nonlinear filtering errors of Markov processes, J. Multivariate Anal. 1 (1971) 365-393. | MR | Zbl

[23] H. Kunita, Ergodic properties of nonlinear filtering processes, in: Alexander K.C., Watkins J.C. (Eds.), Spatial Stochastic Processes, 1991. | MR | Zbl

[24] F. Le Gland, L. Mevel, Exponential forgetting and geometric ergodicity in hidden Markov models, Math. Control Signals Syst. 13 (2000) 63-93. | MR | Zbl

[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. | MR

[26] D. Ocone, Asymptotic stability of Benes filters, Stochastic Anal. Appl. 17 (1999) 1053-1074. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[30] L. Stettner, Invariant measures of pair: State, approximate filtering process, Colloq. Math. LXII (1991) 347-352. | MR | Zbl

[31] H. Totoki, A class of special flows, Z. Wahr. Verw. Geb. 15 (1970) 157-167. | MR | Zbl

[32] H.V. Weizsäcker, Exchanging the order of taking suprema and countable intersections of σ algebras, Ann. Inst. Henri Poincaré B 19 (1) (1983) 91-100. | Numdam | Zbl

[33] D. Williams, Probability with Martingales, Cambridge University Press, 1991. | MR | Zbl

Cité par Sources :