On the stability of interacting processes with applications to filtering and genetic algorithms
Annales de l'I.H.P. Probabilités et statistiques, Tome 37 (2001) no. 2, pp. 155-194.
@article{AIHPB_2001__37_2_155_0,
     author = {Del Moral, Pierre and Guionnet, Alice},
     title = {On the stability of interacting processes with applications to filtering and genetic algorithms},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {155--194},
     publisher = {Elsevier},
     volume = {37},
     number = {2},
     year = {2001},
     mrnumber = {1819122},
     zbl = {0990.60005},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPB_2001__37_2_155_0/}
}
TY  - JOUR
AU  - Del Moral, Pierre
AU  - Guionnet, Alice
TI  - On the stability of interacting processes with applications to filtering and genetic algorithms
JO  - Annales de l'I.H.P. Probabilités et statistiques
PY  - 2001
SP  - 155
EP  - 194
VL  - 37
IS  - 2
PB  - Elsevier
UR  - http://archive.numdam.org/item/AIHPB_2001__37_2_155_0/
LA  - en
ID  - AIHPB_2001__37_2_155_0
ER  - 
%0 Journal Article
%A Del Moral, Pierre
%A Guionnet, Alice
%T On the stability of interacting processes with applications to filtering and genetic algorithms
%J Annales de l'I.H.P. Probabilités et statistiques
%D 2001
%P 155-194
%V 37
%N 2
%I Elsevier
%U http://archive.numdam.org/item/AIHPB_2001__37_2_155_0/
%G en
%F AIHPB_2001__37_2_155_0
Del Moral, Pierre; Guionnet, Alice. On the stability of interacting processes with applications to filtering and genetic algorithms. Annales de l'I.H.P. Probabilités et statistiques, Tome 37 (2001) no. 2, pp. 155-194. http://archive.numdam.org/item/AIHPB_2001__37_2_155_0/

[1] R. Atar, Exponential stability for nonlinear filtering of diffusion processes in a noncompact domain, Ann. Probab. 26 (4) (1998) 1552-1574. | MR | Zbl

[2] R. Atar, O. Zeitouni, Liapunov exponents for finite state space nonlinear filtering, SIAM J. Control Optim. 35 (1) (1997) 36-55. | MR | Zbl

[3] R. Atar, O. Zeitouni, Exponential stability for nonlinear filtering, Ann. Inst. H. Poincare 33 (6) (1997) 697-725. | Numdam | MR | Zbl

[4] R.S. Bucy, Lectures on discrete time filtering, Signal Processing and Digital Filtering, Springer Verlag, 1994. | MR | Zbl

[5] A. Budhiraja, D. Ocone, Exponential stability of discrete time filters for bounded observation noise, Systems and Control Letters 30 (1997) 185-193. | MR | Zbl

[6] D. Crisan, P. Del Moral, T.J. Lyons, Discrete filtering using branching and interacting particle systems, Markov Processes and Related Fields 5 (3) (1999) 293-319. | MR | Zbl

[7] D. Crisan, T.J. Lyons, Nonlinear filtering and measure valued processes, Probab. Theory Related Fields 109 (1997) 217-244. | MR | Zbl

[8] D. Crisan, J. Gaines, T.J. Lyons, A particle approximation of the solution of the Kushner-Stratonovitch equation, SIAM J. Appl. Math. 58 (5) (1998) 1568. | MR | Zbl

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

[10] P. Del Moral, J. Jacod, Interacting Particle Filtering With Discrete Observations, Publications du Laboratoire de Statistiques et Probabilités, Université Paul Sabatier, No 11-99, 1999.

[11] P. Del Moral, Nonlinear filtering using random particles, Theor. Prob. Appl. 40 (4) (1995). | Zbl

[12] P. Del Moral, Non-linear filtering: interacting particle solution, Markov Processes and Related Fields 2 (4) (1996) 555-581. | Zbl

[13] P. Del Moral, Measure valued processes and interacting particle systems. Application to nonlinear filtering problems, Ann. Appl. Probab. 8 (2) (1998) 438-495. | MR | Zbl

[14] P. Del Moral, A uniform theorem for the numerical solving of nonlinear filtering problems, J. Appl. Probab. 35 (1998) 873-884. | MR | Zbl

[15] P. Del Moral, Filtrage non linéaire par systèmes de particules en intéraction, C.R. Acad. Sci. Paris, Série I 325 (1997) 653-658. | Zbl

[16] P. Del Moral, A. Guionnet, Large deviations for interacting particle systems. Applications to nonlinear filtering problems, Stochastic Processes and their Applications 78 (1998) 69-95. | MR | Zbl

[17] P. Del Moral, A. Guionnet, A central limit theorem for nonlinear filtering using interacting particle systems, Ann. Appl. Probab. 9 (2) (1999) 275-297. | MR | Zbl

[18] B. Delyon, O. Zeitouni, Liapunov exponents for filtering problems, in: Davis M.H.A., Elliot R.J. (Eds.), Applied Stochastic Analysis, 1991, pp. 511-521. | MR | Zbl

[19] R.L. Dobrushin, Central limit theorem for nonstationnary Markov chains, I,II, Theory Probab. Appl. 1 (1,4) (1956) 66-80, and 330-385. | Zbl

[20] R.L. Dobrushin, Prescribing a system of random variables by conditional distributions, Theor. Prob. Appl. 15 (3) (1970). | Zbl

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

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

[23] M.F. Norman, Ergodicity of diffusion and temporal uniformity of diffusion approximations, J. Appl. Prob. 14 (1977) 399-404. | MR | Zbl

[24] D.L. Ocone, Topics in nonlinear filtering theory, Ph.D. Thesis, MIT Press, Cambridge, MA, 1980.

[25] 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

[26] E. Pardoux, Filtrage Non Linéaire et Equations aux Dérivés Partielles Stochastiques Associées, Ecole d'été de Probabilités de Saint-Flour XIX-1989, Lecture Notes in Mathematics, 1464, Springer-Verlag, 1991. | MR | Zbl

[27] K.R. Parthasarathy, Probability Measures on Metric Spaces, Academic Press, New York, 1968. | MR | Zbl

[28] J.R. Rowe, Population fixed points for functions of unitation, in: Barzhaf W., Reeves C. (Eds.), Foundations of Genetic Algorithms 5, Morgan Kauffmann, 1999, pp. 69-84.

[29] L. Stettner, On invariant measures of filtering processes, in: Helmes K., Kohlmann N. (Eds.), Stochastic Differential Systems, Proc. 4th Bad Honnef Conference, 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] E. Van Nimwegen, J.P. Crutchfield, M. Michell, Finite populations induce metastability in evolutionary search, Physics Letters A 229 (2) (1997) 144-150. | MR | Zbl

[32] M.D. Vose, Logarithmic convergence of random heuristic search, Evolutionary Computation 4 (4) (1997) 395-404.

[33] M.D. Vose, Modelling simple genetic algorithms, in: Foundations of Genetic Algorithms, Morgan Kaufmann, 1993.

[34] M.D. Vose, Modelling simple genetic algorithms, Elementary Computations 3 (4) (1995) 453-472.

[35] M.D. Vose, G.E. Liepins, Punctuated equilibra in genetic search, Complex Systems 5 (1993) 31-44. | MR | Zbl

[36] M.D. Vose, A.H. Wright, Simple genetic algorithms with linear fitness, Elementary Computations 2 (4) (1995) 347-368.