On the stability of measure valued processes with applications to filtering;Stabilité de processus à valeurs mesures. Application au filtrage

Comptes Rendus de l'Academie des Sciences - Series I: Mathematics

Volumn 329, Issue 5, 1999, Pages 429-434

  Del Moral, Pierre ^a   Guionnet, Alice ^b  

^a UNIVERSITÉ PAUL SABATIER   (France)

^b UNIVERSITÉ PARIS SUD   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033196559     PISSN: 07644442     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0764-4442(00)88619-X     Document Type: Article

References (16)

1. [1] Atar R., Zeitouni O., Liapunov exponents for finite state space non-linear filtering, SIAM J. Control Optim. 35 (1) (1997) 36-55.
2. [2] Atar R., Zeitouni O., Exponential Stability for Nonlinear Filtering, Ann. Inst. H.-Poincaré (1997).
3. [3] Goldberg D.E., Genetic Algorithms and Rule Learning in Dynamic Control Systems, in: Proceedings of the First Int. Conf. on Genetic Algorithms, Lawrence Erlbaum Associates Hillsdale, NJ, 1985, pp. 8-15.
4. [4] Budhiraja A., Ocone D., Exponential stability of discrete time filters for bounded observation noise, Systems and Control Letters 30 (1997) 185-193.
5. [5] Crisan D., Del Moral P., Lyons T.J., Discrete Filtering Using Branching and Interacting Particle Systems, Publ. du Lab. Stastis. Probab., Univ. Paul-Sabatier, No 01-98, 1998.
6. [6] Crisan D., Lyons T.J., Nonlinear Filtering And Measure Valued Processes, Proba. Th. and Rel. Fields 109 (1997) 217-244.
7. [7] Da Prato G., Furhman M., Malliavin P., Asymptotic ergodicity for the Zakai filtering equation, C. R. Acad. Sci. Paris 321 Série I (1995) 613-616.
8. [8] Del Moral P., Measure Valued Processes and Interacting Particle Systems. Application to Non-Linear Filtering Problems, Ann. Appl. Probab. 2 (1998) 438-495.
9. [9] Del Moral P., Guionnet A., Large Deviations for Interacting Particle Systems, Stoch. Proces. Appl. 78 (1998) 69-95.
10. [10] Del Moral P., Guionnet A., A Central Limit Theorem for Non-Linear Filtering using Interacting Particle Systems, Ann. Appl. Probab. (to appear).
11. [11] Del Moral P., Guionnet A., On the Stability of Measure Valued Processes. Applications to Non-Linear Filtering and Interacting Particle Systems, Publ. du Lab. Statis. Probab., Toulouse, No 03-98, 1998.
12. [12] Del Moral P., Jacod J., Protter Ph., The Monte-Carlo Method for filtering with discrete time observations, Publ. du Lab. Probab., Université Paris VI, No 453, 1998.
13. [13] Kunita H., Asymptotic behavior of the non-linear filtering errors of Markov processes, J. Multiv. Anal. 1 (1971) 365-393.
14. [14] Ocone D., Pardoux E., Asymptotic stability of the optimal filter with respect to its initial condition, SIAM J. Control Optim. 34 (1996) 226-243.
15. [15] Stettner L., On invariant measures of filtering processes, in: K. Helmes, N. Kohlmann (Eds.), Stochastic Differential Systems, Proc. 4th Bad Honnef Conf. 1988, Lect. Notes in Control and Inform. SCi., 1989, pp. 279-292.
16. [16] Vose M.D., Wright A.H., Simple genetic algorithms with linear fitness, Element. Comput. 2 (4) (1995) 347-368.