@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}, volume = {37}, year = {2001}, pages = {155-194}, mrnumber = {1819122}, zbl = {0990.60005}, language = {en}, url = {http://dml.mathdoc.fr/item/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) pp. 155-194. http://gdmltest.u-ga.fr/item/AIHPB_2001__37_2_155_0/
[1] Exponential stability for nonlinear filtering of diffusion processes in a noncompact domain, Ann. Probab. 26 (4) (1998) 1552-1574. | MR 1675039 | Zbl 0930.93080
,[2] Liapunov exponents for finite state space nonlinear filtering, SIAM J. Control Optim. 35 (1) (1997) 36-55. | MR 1430282 | Zbl 0940.93073
, ,[3] Exponential stability for nonlinear filtering, Ann. Inst. H. Poincare 33 (6) (1997) 697-725. | Numdam | MR 1484538 | Zbl 0888.93057
, ,[4] Lectures on discrete time filtering, Signal Processing and Digital Filtering, Springer Verlag, 1994. | MR 1288080 | Zbl 0802.93058
,[5] Exponential stability of discrete time filters for bounded observation noise, Systems and Control Letters 30 (1997) 185-193. | MR 1455877 | Zbl 0901.93066
, ,[6] Discrete filtering using branching and interacting particle systems, Markov Processes and Related Fields 5 (3) (1999) 293-319. | MR 1710982 | Zbl 0967.93088
, , ,[7] Nonlinear filtering and measure valued processes, Probab. Theory Related Fields 109 (1997) 217-244. | MR 1477650 | Zbl 0888.93056
, ,[8] A particle approximation of the solution of the Kushner-Stratonovitch equation, SIAM J. Appl. Math. 58 (5) (1998) 1568. | MR 1637870 | Zbl 0915.93060
, , ,[9] Asymptotic ergodicity for the Zakai filtering equation, C.R. Acad. Sci. Paris, Série I 321 (1995) 613-616. | MR 1356563 | Zbl 0838.60039
, , ,[10] Interacting Particle Filtering With Discrete Observations, Publications du Laboratoire de Statistiques et Probabilités, Université Paul Sabatier, No 11-99, 1999.
, ,[11] Nonlinear filtering using random particles, Theor. Prob. Appl. 40 (4) (1995). | Zbl 0860.60030
,[12] Non-linear filtering: interacting particle solution, Markov Processes and Related Fields 2 (4) (1996) 555-581. | Zbl 0879.60042
,[13] Measure valued processes and interacting particle systems. Application to nonlinear filtering problems, Ann. Appl. Probab. 8 (2) (1998) 438-495. | MR 1624949 | Zbl 0937.60038
,[14] A uniform theorem for the numerical solving of nonlinear filtering problems, J. Appl. Probab. 35 (1998) 873-884. | MR 1671237 | Zbl 0940.60060
,[15] Filtrage non linéaire par systèmes de particules en intéraction, C.R. Acad. Sci. Paris, Série I 325 (1997) 653-658. | Zbl 0890.60096
,[16] Large deviations for interacting particle systems. Applications to nonlinear filtering problems, Stochastic Processes and their Applications 78 (1998) 69-95. | MR 1653296 | Zbl 0934.60026
, ,[17] A central limit theorem for nonlinear filtering using interacting particle systems, Ann. Appl. Probab. 9 (2) (1999) 275-297. | MR 1687359 | Zbl 0938.60022
, ,[18] Liapunov exponents for filtering problems, in: , (Eds.), Applied Stochastic Analysis, 1991, pp. 511-521. | MR 1108433 | Zbl 0738.60033
, ,[19] Central limit theorem for nonstationnary Markov chains, I,II, Theory Probab. Appl. 1 (1,4) (1956) 66-80, and 330-385. | Zbl 0093.15001
,[20] Prescribing a system of random variables by conditional distributions, Theor. Prob. Appl. 15 (3) (1970). | Zbl 0264.60037
,[21] Asymptotic behavior of the nonlinear filtering errors of Markov processes, J. Multivariate Analysis 1 (1971) 365-393. | MR 301812 | Zbl 0245.93027
,[22] Ergodic properties nonlinear filtering processes, in: , (Eds.), Spatial Stochastic Processes, 1991. | MR 1144099 | Zbl 0742.60062
,[23] Ergodicity of diffusion and temporal uniformity of diffusion approximations, J. Appl. Prob. 14 (1977) 399-404. | MR 436355 | Zbl 0365.60070
,[24] Topics in nonlinear filtering theory, Ph.D. Thesis, MIT Press, Cambridge, MA, 1980.
,[25] Asymptotic stability of the optimal filter with respect to its initial condition, SIAM J. Control Optim. 34 (1996) 226-243. | MR 1372912 | Zbl 1035.93508
, ,[26] 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 1108184 | Zbl 0732.60050
,[27] Probability Measures on Metric Spaces, Academic Press, New York, 1968. | MR 226684 | Zbl 0153.19101
,[28] Population fixed points for functions of unitation, in: , (Eds.), Foundations of Genetic Algorithms 5, Morgan Kauffmann, 1999, pp. 69-84.
,[29] On invariant measures of filtering processes, in: , (Eds.), Stochastic Differential Systems, Proc. 4th Bad Honnef Conference, 1988, Lecture Notes in Control and Inform. Sci., 1989, pp. 279-292. | MR 1236074 | Zbl 0683.93082
,[30] Invariant measures of pair state/approximate filtering process, Colloq. Math. LXII (1991) 347-352. | MR 1142935 | Zbl 0795.60028
,[31] Finite populations induce metastability in evolutionary search, Physics Letters A 229 (2) (1997) 144-150. | MR 1445497 | Zbl 1043.92516
, , ,[32] Logarithmic convergence of random heuristic search, Evolutionary Computation 4 (4) (1997) 395-404.
,[33] Modelling simple genetic algorithms, in: Foundations of Genetic Algorithms, Morgan Kaufmann, 1993.
,[34] Modelling simple genetic algorithms, Elementary Computations 3 (4) (1995) 453-472.
,[35] Punctuated equilibra in genetic search, Complex Systems 5 (1993) 31-44. | MR 1116420 | Zbl 0764.68149
, ,[36] Simple genetic algorithms with linear fitness, Elementary Computations 2 (4) (1995) 347-368.
, ,