Branching and interacting particle systems. Approximations of Feynman-Kac formulae with applications to non-linear filtering

Pierre Del Moral; Laurent Miclo

Séminaire de probabilités de Strasbourg (2000)

  • Volume: 34, page 1-145

How to cite

top

Del Moral, Pierre, and Miclo, Laurent. "Branching and interacting particle systems. Approximations of Feynman-Kac formulae with applications to non-linear filtering." Séminaire de probabilités de Strasbourg 34 (2000): 1-145. <http://eudml.org/doc/114038>.

@article{DelMoral2000,
author = {Del Moral, Pierre, Miclo, Laurent},
journal = {Séminaire de probabilités de Strasbourg},
keywords = {nonlinear filtering; interacting particle systems; Feynman-Kac formulae},
language = {eng},
pages = {1-145},
publisher = {Springer - Lecture Notes in Mathematics},
title = {Branching and interacting particle systems. Approximations of Feynman-Kac formulae with applications to non-linear filtering},
url = {http://eudml.org/doc/114038},
volume = {34},
year = {2000},
}

TY - JOUR
AU - Del Moral, Pierre
AU - Miclo, Laurent
TI - Branching and interacting particle systems. Approximations of Feynman-Kac formulae with applications to non-linear filtering
JO - Séminaire de probabilités de Strasbourg
PY - 2000
PB - Springer - Lecture Notes in Mathematics
VL - 34
SP - 1
EP - 145
LA - eng
KW - nonlinear filtering; interacting particle systems; Feynman-Kac formulae
UR - http://eudml.org/doc/114038
ER -

References

top
  1. [1] J. Abela, D. Abramson, A. De Silval, M. Krishnamoorthy, and G. Mills. Computing optimal schedules for landing aircraft. Technical report, Department of Computer Systems Eng. R.M.I.T., Melbourne, May 1993. 
  2. [2] J.-M. Alliot, D. Delahaye, J.-L. Farges, and M. Schoenauer. Genetic algorithms for automatic regrouping of air traffic control sectors. In J. R. McDonnell, R. G. Reynolds, and D. B. Fogel, editors, Proceedings of the 4th Annual Conference on Evolutionary Programming, pages 657-672. MIT Press, March 1995. 
  3. [3] G. Ben Arous and M. Brunaud. Methode de laplace : étude variationnelle des fluctuations de diffusions de type "champ moyen". Stochastics, 31-32:79-144, 1990. Zbl0705.60046MR1080535
  4. [4] R. Atar and O. Zeitouni. Exponential stability for nonlinear filtering. Annales de l'Institut Henri Poincaré, 33(6):697-725, 1997. Zbl0888.93057MR1484538
  5. [5] R. Atar and O. Zeitouni. Lyapunov exponents for finite state space nonlinear filtering. Society for Industrial and Applied Mathematics. Journal on Control and Optimization, 35(1):36-55, January 1997. Zbl0940.93073MR1430282
  6. [6] J. Baker. Adaptative selection methods for genetic algorithms. In J. Grefenstette, editor, Proc. International Conf. on Genetic Algorithms and their Applications. L. Erlbaum Associates, 1985. 
  7. [7] J. Baker. Reducing bias and inefficiency in the selection algorithm. In J. Grefenstette, editor, Proc. of the Second International Conf. on Genetic Algorithms and their Applications. L. Erlbaum Associates, 1987. 
  8. [8] A. Bakirtzis, S. Kazarlis, and V. Petridis. A genetic algorithm solution to the economic dispatch problem. http://www.dai.ed.ac.uk/groups/evalg/eag_local_copies_of_papers.body.html. 
  9. [9] D. Bakry. L'hypercontractivité et son utilisation en théorie des semigroupes. In P. Bernard, editor,Lectures on Probability Theory. Ecole d'Eté de Probabilités de Saint-Flour XXII-1992, Lecture Notes in Mathematics1581. Springer-Verlag, 1994. Zbl0856.47026MR1307413
  10. [10] P. Barbe and P. Bertail. The Weighted Bootstrap. Lecture Notes in Statistics98. Springer-Verlag, 1995. Zbl0826.62030
  11. [11] E. Beadle and P. Djuric. A fast weighted Bayesian bootstrap filter for nonlinear model state estimation. Institute of Electrical and Electronics Engineers. Transactions on Aerospace and Electronic Systems, AES-33:338-343, January 1997. 
  12. [12] B.E. Benes. Exact finite-dimensional filters for certain diffusions with nonlinear drift. Stochastics, 5:65-92, 1981. Zbl0458.60030MR643062
  13. [13] E. Bolthausen. Laplace approximation for sums of independent random vectors i. Probability Theory and Related Fields, 72:305-318, 1986. Zbl0572.60007MR836280
  14. [14] C.L. Bridges and D.E. Goldberg. An analysis of reproduction and crossover in a binary-coded genetic algorithm. In J.J. Grefenstette, editor, Proc. of the Second International Conf. on Genetic Algorithms and their Applications. L. Erlbaum Associates, 1987. 
  15. [15] R.S. Bucy. Lectures on discrete time filtering, Signal Processing and Digital Filtering. Springer-Verlag, 1994. Zbl0802.93058MR1288080
  16. [16] A. Budhiraja and D. Ocone. Exponential stability of discrete time filters for bounded observation noise. Systems and Control Letters, 30:185-193, 1997. Zbl0901.93066MR1455877
  17. [17] Z. Cai, F. Le Gland, and H. Zhang. An adaptative local grid refinement method for nonlinear filtering. Technical report, INRIA, October 1995. 
  18. [18] H. Carvalho, P. Del Moral, A. Monin, and G. Salut. Optimal nonlinear filtering in gps/ins integration. Institute of Electrical and Electronics Engineers. Transactions on Aerospace and Electronic Systems, 33(3):835-850, July 1997. 
  19. [19] R. Cerf. Une théorie asymptotique des algorithmes génétiques. Thèse de doctorat, Université Montpellier II, March 1994. 
  20. [20] M. Chaleyat-Maurel and D. Michel. Des résultats de non existence de filtres de dimension finie. Comptes Rendus de l'Académie des Sciences de Paris. Série I. Mathématique, 296, 1983. Zbl0529.60038MR719280
  21. [21] D. Crisan, J. Gaines, and T.J. Lyons. A particle approximation of the solution of the kushner-stratonovitch equation. Society for Industrial and Applied Mathematics. Journal on Applied Mathematics, 58(5):1568-1590, 1998. Zbl0915.93060MR1637870
  22. [22] D. Crisan and M. Grunwald. Large deviation comparison of branching algorithms versus resampling algorithm. Preprint, 1998. 
  23. [23] D. Crisan and T.J. Lyons. Nonlinear filtering and measure valued processes. Probability Theory and Related Fields, 109:217-244, 1997. Zbl0888.93056MR1477650
  24. [24] D. Crisan, P. Del Moral, and T.J. Lyons. Interacting particle systems approximations of the Kushner-Stratonovitch equation. Advances in Applied Probability, 31(3), September 1999. Zbl0947.60040MR1742696
  25. [25] D. Crisan, P. Del Moral, and T.J. Lyons. Non linear filtering using branching and interacting particle systems. Markov Processes and Related Fields, 5(3):293-319, 1999. Zbl0967.93088MR1710982
  26. [26] G. Da Prato, M. Furhman, and P. Malliavin. Asymptotic ergodicity for the Zakai filtering equation. Comptes Rendus de l'Académie des Sciences de Paris. Série I. Mathématique, 321(5):613-616, 1995. Zbl0838.60039MR1356563
  27. [27] E.B. Davies. Heat Kernels and Spectral Theory. Cambridge University Press, 1989. Zbl0699.35006MR990239
  28. [28] M. Davis. New approach to filtering for nonlinear systems. Institute of Electrical and Electronics Engineers. Proceedings, 128(5):166-172, 1981. Part D. MR631971
  29. [29] D. Dawson. Measure-valued Markov processes. In P.L. Hennequin, editor, Lectures on Probability Theory. Ecole d'Eté de Probabilités de Saint-Flour XXI-1991, Lecture Notes in Mathematics1541. Springer-Verlag, 1993. Zbl0799.60080MR1242575
  30. [30] P. Del Moral. Non-linear filtering: interacting particle resolution. Markov Processes and Related Fields, 2(4):555-581, 1996. Zbl0879.60042MR1405150
  31. [31] P. Del Moral. Filtrage non linéaire par systèmes de particules en interaction. Comptes Rendus de l'Académie des Sciences de Paris. Série I. Mathématique, 325:653-658, 1997. Zbl0890.60096
  32. [32] P. Del Moral. Maslov optimization theory: optimality versus randomness. In V.N. Kolokoltsov and V.P. Maslov, editors, Idempotency Analysis and its Applications, Mathematics and its Applications401, pages 243-302. Kluwer Academic Publishers, Dordrecht/Boston/London, 1997. MR1447629
  33. [33] P. Del Moral. Measure valued processes and interacting particle systems. Application to non linear filtering problems. The Annals of Applied Probability, 8(2):438-495, 1998. Zbl0937.60038MR1624949
  34. [34] P. Del Moral. A uniform convergence theorem for the numerical solving of non linear filtering problems. Journal of Applied Probability, 35:873-884, 1998. Zbl0940.60060MR1671237
  35. [35] P. Del Moraland A. Guionnet. Large deviations for interacting particle systems. Applications to non linear filtering problems. Stochastic Processes and their Applications, 78:69-95, 1998. Zbl0934.60026MR1653296
  36. [36] P. Del Moral and A. Guionnet. On the stability of measure valued processes. Applications to non linear filtering and interacting particle systems. Publications du Laboratoire de Statistique et Probabilités, no 03-98, Université Paul Sabatier, 1998. MR1710091
  37. [37] P. Del Moraland A. Guionnet. A central limit theorem for non linear filtering using interacting particle systems. The Annals of Applied Probability, 9(2):275-297, 1999. Zbl0938.60022MR1687359
  38. [38] P. Del Moraland A. Guionnet. On the stability of measure valued processes with applications to filtering. Comptes Rendus de l'Académie des Sciences de Paris. Série I. Mathématique, 329:429-434, 1999. Zbl0935.92001MR1710091
  39. [39] P. Del Moral and J. Jacod. Interacting particle filtering with discrete observations. Publications du Laboratoire de Statistiques et Probabilités, no 11-99, 1999. 
  40. [40] P. Del Moral and J. Jacod. The monte-carlo method for filtering with discrete time observations. central limit theorems. Publications du Laboratoire de Probabilités, no 515, 1999. 
  41. [41] P. Del Moral, J. Jacod, and P. Protter. The Monte Carlo method for filtering with discrete time observations. Publications du Laboratoire de Probabilités, no 453, June 1998. Zbl0979.62072
  42. [42] P. Del Moral and M. Ledoux. Convergence of empirical processes for interacting particle systems with applications to nonlinear filtering. to appear in Journal of Theoretical Probability, January 2000. Zbl0954.60014MR1744985
  43. [43] P. Del Moral and L. Miclo. Asymptotic stability of non linear semigroup of Feynman-Kac type. Préprint, publications du Laboratoire de Statistique et Probabilités, no 04-99, 1999. 
  44. [44] P. Del Moral and L. Miclo. On the convergence and the applications of the generalized simulated annealing. SIAM Journal on Control and Optimization, 37(4):1222-1250, 1999. Zbl0928.60046MR1691939
  45. [45] P. Del Moral and L. Miclo. A Moran particle system approximation of Feynman-Kac formulae. to appear in Stochastic Processes and their Applications, 2000. Zbl1030.65004MR1741805
  46. [46] P. Del Moral, J.C. Noyer, and G. Salut. Résolution particulaire et traitement non-linéaire du signal : application radar/sonar. In Traitement du signal, September 1995. Zbl0885.94004
  47. [47] P. Del Moral, G. Rigal, and G. Salut. Estimation et commande optimale non linéaire. Technical Report 2, LAAS/CNRS, March 1992. Contract D.R.E.T.-DIGILOG. 
  48. [48] B. Delyon and O. Zeitouni. Liapunov exponents for filtering problems. In M.H.A. Davis and R.J. Elliot, editors, Applied Stochastic Analysis, pages 511-521. Springer-Verlag, 1991. Zbl0738.60033MR1108433
  49. [49] A. Dembo and O. Zeitouni. Large Deviations Techniques and Application. Jones and Bartlett, 1993. Zbl0793.60030MR1202429
  50. [50] A.N. Van der Vaart and J.A. Wellner. Weak Convergence and Empirical Processes with Applications to Statistics. Springer Series in Statistics. Springer, 1996. Zbl0862.60002MR1385671
  51. [51] J.-D. Deuschel and D.W. Stroock. Large Deviations. Pure and applied mathematics137. Academic Press, 1989. Zbl0705.60029MR997938
  52. [52] P. Diaconis and B. Efron. Méthodes de calculs statistiques intensifs sur ordinateurs. Pour la Science, 1983. translation of the American Scientist. 
  53. [53] R.L. Dobrushin. Central limit theorem for nonstationnary Markov chains, i,ii. Theory of Probability and its Applications, 1(1 and 4):66-80 and 330-385, 1956. Zbl0093.15001MR86436
  54. [54] E.B. Dynkin and A. Mandelbaum. Symmetric statistics, Poisson processes and multiple Wiener integrals. The Annals of Statistics, 11:739-745, 1983. Zbl0518.60050MR707925
  55. [55] S. Ethier and T. Kurtz. Markov Processes, Characterization and Convergence. Wiley series in probability and mathematical statistics. John Wiley and Sons, New York, 1986. Zbl0592.60049MR838085
  56. [56] M. Fujisaki, G. Kallianpur, and H. Kunita. Stochastic differential equations for the non linear filtering problem. Osaka J. Math., 1:19-40, 1972. Zbl0242.93051MR336801
  57. [57] F. Le Gland. Monte-Carlo methods in nonlinear filtering. In Proceedings of the 23rd IEEE Conference on Decision and Control, pages 31-32, Las Vegas, December 1984. 
  58. [58] F. Le Gland. High order time discretization of nonlinear filtering equations. In 28th IEEE CDC, pages 2601-2606, Tampa, 1989. MR1039100
  59. [59] F. Le Gland, C. Musso, and N. Oudjane. An analysis of regularized interacting particle methods for nonlinear filtering. In Proceedings of the 3rd IEEE European Workshop on Computer-Intensive Methods in Control and Signal Processing, Prague, September 1998. Zbl1056.93588
  60. [60] D.E. Goldberg. Genetic algorithms and rule learning in dynamic control systems. In Proceedings of the First International Conference on Genetic Algorithms, pages 8-15, Hillsdale, NJ, 1985. L. Erlbaum Associates. Zbl0675.68045
  61. [61] D.E. Goldberg. Simple genetic algorithms and the minimal deceptive problem. In L. Davis, editorGenetic Algorithms and Simulated Annealing. Pitman, 1987. 
  62. [62] D.E. Goldberg. Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley, Reading, MA, 1989. Zbl0721.68056
  63. [63] D.E. Goldberg and P. Segrest. Finite Markov chain analysis of genetic algorithms. In J.J. Grefenstette, editor, Proc. of the 2nd Int. Conf. on Genetic Algorithms. L. Erlbaum Associates, 1987. 
  64. [64] N.J. Gordon, D.J. Salmon, and A.F.M. Smith. Novel approach to nonlinear/non-Gaussian Bayesian state estimation. IEE Proceedings F, 140:107-113, 1993. 
  65. [65] C. Graham and S. Méléard. Stochastic particle approximations for generalized Boltzmann models and convergence estimates. The Annals of Probability, 25(1):115-132, 1997. Zbl0873.60076MR1428502
  66. [66] A. Guionnet. About precise Laplace's method; applications to fluctuations for mean field interacting particles. Preprint, 1997. 
  67. [67] J.H. Holland. Adaptation in Natural and Artificial Systems. University of Michigan Press, Ann Arbor, 1975. Zbl0317.68006MR441393
  68. [68] J. Jacod and A.N. Shiryaev. Limit Theorems for Stochastic Processes. A Series of Comprehensive Studies in Mathematics288. Springer-Verlag, 1987. Zbl0635.60021MR959133
  69. [69] J.M. Johnson and Y. Rahmat-Samii. Genetic algorithms in electromagnetics. In IEEE Antennas and Propagation Society International Symposium Digest, volume 2, pages 1480-1483, 1996. 
  70. [70] F. Jouve, L. Kallel, and M. Schoenauer. Mechanical inclusions identification by evolutionary computation. European Journal of Finite Elements, 5(5-6):619-648, 1996. Zbl0924.73321MR1436837
  71. [71] F. Jouve, L. Kallel, and M. Schoenauer. Identification of mechanical inclusions. In D. Dagsgupta and Z. Michalewicz, editors, Evolutionary Computation in Engeneering, pages 477-494. Springer Verlag, 1997. Zbl0924.73321
  72. [72] G. Kallianpur and C. Striebel. Stochastic differential equations occuring in the estimation of continuous parameter stochastic processes. Tech. Rep. 103, Department of statistics, Univ. of Minnesota, September 1967. Zbl0195.44503
  73. [73] G. Kitagawa. Monte-Carlo filter and smoother for non-Gaussian nonlinear state space models. Journal on Computational and Graphical Statistics, 5(1):1-25, 1996. MR1380850
  74. [74] H. Korezlioglu. Computation of filters by sampling and quantization. Technical Report 208, Center for Stochastic Processes, University of North Carolina, 1987. 
  75. [75] H. Korezlioglu and G. Maziotto. Modelization and filtering of discrete systems and discrete approximation of continuous systems. In Modélisation et Optimisation des Systèmes, VI Conférence INRIA, Nice, 1983. 
  76. [76] H. Korezlioglu and W.J. Runggaldier. Filtering for nonlinear systems driven by nonwhite noises: an approximating scheme. Stochastics and Stochastics Reports, 44(1-2):65-102, 1993. Zbl0786.60058MR1276930
  77. [77] H. Kunita. Asymptotic behavior of nonlinear filtering errors of Markov processes. Journal of Multivariate Analysis, 1(4):365-393, 1971. Zbl0245.93027MR301812
  78. [78] H. Kunita. Ergodic properties nonlinear filtering processes. In K.C. Alexander and J.C. Watkins, editors, Spatial Stochastic Processes. Birkhaüser Boston, Boston, MA, 1991. Zbl0742.60062MR1144099
  79. [79] S. Kusuoda and Y. . Tamura. Gibbs measures for mean field potentials. J. Fac. Sci. Univ. Tokyo, Sect. IA, Math, 31, 1984. Zbl0549.60099MR743526
  80. [80] J.W. Kwiatkowski. Algorithms for index tracking. Technical report, Department of Business Studies, The University of Edinburgh, 1991. Zbl0765.90012MR1263832
  81. [81] R.S. Liptser and A.N. Shiryayev. Theory of Martingales. Dordrecht: Kluwer Academic Publishers, 1989. Zbl0728.60048MR1022664
  82. [82] G.B. Di Masi, M. Pratelli, and W.G. Runggaldier. An approximation for the nonlinear filtering problem with error bounds. Stochastics, 14(4):247-271, 1985. Zbl0566.60046MR805124
  83. [83] S. Méléard. Asymptotic behaviour of some interacting particle systems; McKean-Vlasov and Boltzmann models. In D. Talay and L. Tubaro, editors, Probabilistic Models for Nonlinear Partial Differential Equations, Montecatini Terme, 1995, Lecture Notes in Mathematics1627. Springer-Verlag, 1996. Zbl0864.60077MR1431299
  84. [84] C. Musso and N. Oudjane. Regularization schemes for branching particle systems as a numerical solving method of the nonlinear filtering problem. In Proceedings of the Irish Signals Systems Conference, Dublin, June 1998. MR1722661
  85. [85] C. Musso and N. Oudjane. Regularized particle schemes applied to the tracking problem. In International Radar Symposium, Munich, Proceedings, September 1998. 
  86. [86] Y. Nishiyama. Some central limit theorems for l∞-valued semimartingales and their applications. Probability Theory and Related Fields, 108:459-494, 1997. Zbl0895.60025MR1465638
  87. [87] A. Nix and M.D. Vose. Modelling genetic algorithms with Markov chains. Annals of Mathematics and Artificial Intelligence, 5:79-88, 1991. Zbl1034.68534MR1279417
  88. [88] D. Ocone and E. Pardoux. Asymptotic stability of the optimal filter with respect to its initial condition. Society for Industrial and Applied Mathematics.Journal on Control and Optimization, 34:226-243, 1996. Zbl1035.93508MR1372912
  89. [89] D.L. Ocone. Topics in nonlinear filtering theory. Phd thesis, MIT, Cambridge, 1980. 
  90. [90] E. Pardoux. Filtrage non linéaire et équations aux dérivés partielles stochastiques associées. In P.L. Hennequin, editor, Ecole d'Eté de Probabilités de Saint-Flour XIX-1989, Lecture Notes in Mathematics1464. Springer-Verlag, 1991. Zbl0732.60050MR1108184
  91. [91] E. Pardoux and D. Talay. Approximation and simulation of solutions of stochastic differential equations. Acta Applicandae Mathematicae, 3(1):23-47, 1985. Zbl0554.60062MR773336
  92. [92] J. Picard. Approximation of nonlinear filtering problems and order of convergence. In Filtering and Control of Random Processes, Lecture Notes Control and Inf. Sc.61. Springer, 1984. Zbl0539.93078MR874832
  93. [93] J. Picard. An estimate of the error in time discretization of nonlinear filtering problems. In C.I. Byrnes and A. Lindquist, editors, Proceedings of the 7th MTNS — Theory and Applications of nonlinear Control Systems, Stockholm, 1985, pages 401-412, Amsterdam, 1986. North-Holland Pub. Zbl0615.93068MR935393
  94. [94] J. Picard. Nonlinear filtering of one-dimensional diffusions in the case of a high signal-to-noise ratio. Society for Industrial and Applied Mathematics. Journal on Applied Mathematics, 16:1098-1125, 1986. Zbl0617.93057MR866283
  95. [95] S.T. Rachev. Probability Metrics and the Stability of Stochastic Models. Wiley, New York, 1991. Zbl0744.60004MR1105086
  96. [96] D. Revuz and M. Yor. Continuous Martingales and Brownian Motion. Springer-Verlag, 1991. Zbl0731.60002MR1083357
  97. [97] J. Shapcott. Index tracking: genetic algorithms for investment portfolio selection. Technical Report SS92-24, EPCC, September 1992. 
  98. [98] T. Shiga and H. Tanaka. Central limit theorem for a system of markovian particles with mean field interaction. Zeitschrift für Wahrscheinlichkeitstheorie verwandte Gebiete, 69, 1985. 439-459. Zbl0607.60095MR787607
  99. [99] A.N. Shiryaev. On stochastic equations in the theory of conditional Markov processes. Theor. Prob. Appl., 11:179-184, 1966. 
  100. [100] A.N. Shiryaev. Probability. Number 95 in Graduate Texts in Mathematics. Springer-Verlag, New-York, second edition, 1996. Zbl0835.60002MR1368405
  101. [101] B. Simon. Trace ideals and their applications. London Mathematical Society Lecture Notes Series 35. Cambridge University Press, 1977. Zbl0423.47001MR541149
  102. [102] L. Stettner. On invariant measures of filtering processes. In K. Helmes and N. Kohlmann, editors, Stochastic Differential Systems, Proc. 4th Bad Honnef Conf. , Lecture Notes in Control and Inform. Sci., pages 279-292, 1989. Zbl0683.93082MR1236074
  103. [103] L. Stettner. Invariant measures of pair state/approximate filtering process. In Colloq. Math. LXII, pages 347-352, 1991. Zbl0795.60028MR1142935
  104. [104] R.L. Stratonovich. Conditional Markov processes. Theor. Prob. Appl., 5:156-178, 1960. Zbl0106.12401MR137157
  105. [105] D. Stroock and S.R.S. Varadhan. Multidimensional Diffusion Processes. Springer-Verlag, 1979. Zbl0426.60069MR532498
  106. [106] D.W. Stroock. An Introduction to the Theory of Large Deviations. Universitext. Springer-Verlag, New-York, 1984. Zbl0552.60022MR755154
  107. [107] M. Talagrand. Sharper bounds for Gaussian and empirical processes. The Annals of Probability, 22:28-76, 1994. Zbl0798.60051MR1258865
  108. [108] D. Talay. Efficient numerical schemes for the approximation of expectations of functionals of the solution of s.d.e. and applications. In Filtering and Control of random processes (Paris, 1983), Lecture Notes in Control and Inform. Sci.61, pages 294-313, Berlin-New York, 1984. Springer. Zbl0542.93077MR874837
  109. [109] H. Tanaka. Limit theorems for certain diffusion processes. In Proceedings of the Taniguchi Symp., Katata, 1982, pages 469-488, Tokyo, 1984. Kinokuniya. Zbl0552.60051MR780770
  110. [110] D. Treyer, D.S. Weile, and E. Michielsen. The application of novel genetic algorithms to electromagnetic problems. In Applied Computational Electromagnetics, Symposium Digest, volume 2, pages 1382-1386, Monterey, CA, March 1997. 
  111. [111] M.D. Vose. The Simple Genetic Algorithm, Foundations and Theory. The MIT Press Books, August 1999. Zbl0952.65048MR1713436
  112. [112] D. Williams. Probability with Martingales. Cambridge Mathematical Textbooks, 1992. Zbl0722.60001MR1155402

Citations in EuDML Documents

top
  1. Pierre Del Moral, L. Miclo, Particle approximations of Lyapunov exponents connected to Schrödinger operators and Feynman–Kac semigroups
  2. Pierre Del Moral, Laurent Miclo, On the stability of nonlinear Feynman-Kac semigroups
  3. Mathias Rousset, On a probabilistic interpretation of shape derivatives of Dirichlet groundstates with application to Fermion nodes
  4. Pierre Del Moral, L. Miclo, Particle approximations of Lyapunov exponents connected to Schrödinger operators and Feynman–Kac semigroups
  5. Mohamed El Makrini, Benjamin Jourdain, Tony Lelièvre, Diffusion Monte Carlo method: Numerical Analysis in a Simple Case
  6. Pierre Del Moral, Arnaud Doucet, Sumeetpal S. Singh, A backward particle interpretation of Feynman-Kac formulae
  7. François Bolley, Arnaud Guillin, Florent Malrieu, Trend to equilibrium and particle approximation for a weakly selfconsistent Vlasov-Fokker-Planck equation
  8. Pierre Del Moral, Laurent Miclo, Dynamiques recuites de type Feynman-Kac : résultats précis et conjectures
  9. Pierre Del Moral, Nicolas G. Hadjiconstantinou, An introduction to probabilistic methods with applications

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.