Free access
Issue
ESAIM: M2AN
Volume 44, Number 5, September-October 2010
Special Issue on Probabilistic methods and their applications
Page(s) 947 - 975
DOI http://dx.doi.org/10.1051/m2an/2010048
Published online 26 August 2010
  1. D. Bakry, L'hypercontractivitée et son utilisation en théorie des semigroupes, in Lecture Notes in Math. 1581, École d'été de St. Flour XXII, P. Bernard Ed. (1992).
  2. P. Billingsley, Probability and Measure. Third edition, Wiley series in probability and mathematical statistics (1995).
  3. E. Cancès, B. Jourdain and T. Lelièvre, Quantum Monte Carlo simulations of fermions. A mathematical analysis of the fixed-node approximation. ESAIM: M2AN 16 (2006) 1403–1449.
  4. F. Cerou, P. Del Moral and A. Guyader, A non asymptotic variance theorem for unnormalized Feynman-Kac particle models. Ann. Inst. Henri Poincaré (to appear).
  5. P.-A. Coquelin, R. Deguest and R. Munos, Numerical methods for sensitivity analysis of Feynman-Kac models. Available at http://hal.inria.fr/inria-00336203/en/, HAL-INRIA Research Report 6710 (2008).
  6. D. Crisan, P. Del Moral and T. Lyons, Interacting Particle Systems. Approaximations of the Kushner-Stratonovitch Equation. Adv. Appl. Probab. 31 (1999) 819–838. [CrossRef]
  7. P. Del Moral, Feynman-Kac formulae. Genealogical and interacting particle systems with applications. Probability and its Applications, Springer Verlag, New York (2004).
  8. P. Del Moral and A. Doucet, Particle motions in absorbing medium with hard and soft obstacles. Stoch. Anal. Appl. 22 (2004) 1175–1207. [CrossRef] [MathSciNet]
  9. P. Del Moral and L. Miclo, Branching and interacting particle systems approximations of Feynman-Kac formulae with applications to non-linear filtering, in Séminaire de Probabilités XXXIV, Lecture Notes in Math. 1729, Springer, Berlin (2000) 1–145.
  10. P. Del Moral and L. Miclo, Particle approximations of Lyapunov exponents connected to Schroedinger operators and Feynman-Kac semigroups. ESAIM: PS 7 (2003) 171–208. [CrossRef] [EDP Sciences]
  11. P. Del Moral and E. Rio, Concentration inequalities for mean field particle models. Available at http://hal.inria.fr/inria-00375134/fr/, HAL-INRIA Research Report 6901 (2009).
  12. P. Del Moral, J. Jacod and P. Protter, The Monte Carlo Method for filtering with discrete-time observations. Probab. Theory Relat. Fields 120 (2001) 346–368. [CrossRef]
  13. P. Del Moral, A. Doucet and S.S. Singh, Forward smoothing using sequential Monte Carlo. Cambridge University Engineering Department, Technical Report CUED/F-INFENG/TR 638 (2009).
  14. G.B. Di Masi, M. Pratelli and W.G. Runggaldier, An approximation for the nonlinear filtering problem with error bounds. Stochastics 14 (1985) 247–271. [MathSciNet]
  15. R. Douc, A. Garivier, E. Moulines and J. Olsson, On the forward filtering backward smoothing particle approximations of the smoothing distribution in general state spaces models. Technical report, available at arXiv:0904.0316.
  16. A. Doucet, N. De Freitas and N. Gordon Eds., Sequential Monte Carlo Methods in Pratice. Statistics for engineering and Information Science, Springer, New York (2001).
  17. M. El Makrini, B. Jourdain and T. Lelièvre, Diffusion Monte Carlo method: Numerical analysis in a simple case. ESAIM: M2AN 41 (2007) 189–213. [CrossRef] [EDP Sciences]
  18. M. Émery, Stochastic calculus in manifolds. Universitext, Springer-Verlag, Berlin (1989).
  19. S.J. Godsill, A. Doucet and M. West, Monte Carlo smoothing for nonlinear time series. J. Am. Stat. Assoc. 99 (2004) 156–168. [CrossRef]
  20. N. Ikeda and S. Watanabe, Stochastic differential equations and diffusion processes 24. Second edition, North-Holland Mathematical Library, North-Holland Publishing Co., Amsterdam (1989).
  21. M. Kac, On distributions of certain Wiener functionals. Trans. Am. Math. Soc. 65 (1949) 1–13.
  22. G. Kallianpur and C. Striebel, Stochastic differential equations occurring in the estimation of continuous parameter stochastic processes. Tech. Rep. 103, Department of Statistics, University of Minnesota, Minneapolis (1967).
  23. N. Kantas, A. Doucet, S.S. Singh and J.M. Maciejowski, An overview of sequential Monte Carlo methods for parameter estimation in general state-space models, in Proceedings IFAC System Identification (SySid) Meeting, available at http://publications.eng.cam.ac.uk/16156/ (2009).
  24. H. Korezlioglu and W.J. Runggaldier, Filtering for nonlinear systems driven by nonwhite noises: an approximating scheme. Stoch. Stoch. Rep. 44 (1983) 65–102.
  25. J. Picard, Approximation of the nonlinear filtering problems and order of convergence, in Filtering and control of random processes, Lecture Notes in Control and Inf. Sci. 61, Springer (1984) 219–236.
  26. G. Poyiadjis, A. Doucet and S.S. Singh, Sequential Monte Carlo computation of the score and observed information matrix in state-space models with application to parameter estimation. Technical Report CUED/F-INFENG/TR 628, Cambridge University Engineering Department (2009).
  27. D. Revuz, Markov chains. North-Holland (1975).
  28. M. Rousset, On the control of an interacting particle approximation of Schroedinger ground states. SIAM J. Math. Anal. 38 (2006) 824–844. [CrossRef] [MathSciNet]
  29. A.N. Shiryaev, Probability, Graduate Texts in Mathematics 95. Second edition, Springer (1986).
  30. D.W. Stroock, Probability Theory: an Analytic View. Cambridge University Press, Cambridge (1994).
  31. D.W. Stroock, An Introduction to Markov Processes, Graduate Texts in Mathematics 230. Springer (2005).

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