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Book Review

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MathSciNet review: 2791780
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Book Information:

Authors: Alan Bain and Dan Crisan
Title: Fundamentals of stochastic filtering
Additional book information: Stochastic Modelling and Applied Probability, 60, Springer, New York, 2009, xiv+390 pp., ISBN 978-0-387-76895-3

References [Enhancements On Off] (What's this?)

  • 1. J. M. C. Clark and D. Crisan, On a robust version of the integral representation formula of nonlinear filtering, Probab. Theory Related Fields 133 (2005), no. 1, 43–56. MR 2197136,
  • 2. J. M. C. Clark, The design of robust approximations to the stochastic differential equations of nonlinear filtering, Communication systems and random process theory (Proc. 2nd NATO Advanced Study Inst., Darlington, 1977) Sijthoff & Noordhoff, Alphen aan den Rijn, 1978, pp. 721–734. NATO Advanced Study Inst. Ser., Ser. E: Appl. Sci., No. 25. MR 0529130
  • 3. P. Del Moral, A. Doucet and S. S. Singh A Backward Particle Interpretation of Feynman-Kac Formulae, HAL-INRIA RR-7019 (07-2009); M2AN, vol 44, no. 5, 947-976 (Sept. 2010).
  • 4. P. Del Moral and L. Miclo, Branching and interacting particle systems approximations of Feynman-Kac formulae with applications to non-linear filtering, Séminaire de Probabilités, XXXIV, Lecture Notes in Math., vol. 1729, Springer, Berlin, 2000, pp. 1–145. MR 1768060,
  • 5. Pierre Del Moral, Feynman-Kac formulae, Probability and its Applications (New York), Springer-Verlag, New York, 2004. Genealogical and interacting particle systems with applications. MR 2044973
  • 6. P. Del Moral and E. Rio, ``Concentration Inequalities for Mean Field Particle Models'', HAL-INRIA RR-6901, 2009; to appear in Annals of Applied Probability (2010-2011).
  • 7. Arnaud Doucet, Nando de Freitas, and Neil Gordon (eds.), Sequential Monte Carlo methods in practice, Statistics for Engineering and Information Science, Springer-Verlag, New York, 2001. MR 1847783
  • 8. Stewart N. Ethier and Thomas G. Kurtz, Markov processes, Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics, John Wiley & Sons, Inc., New York, 1986. Characterization and convergence. MR 838085
  • 9. T. E. Harris and H. Kahn. Estimation of particle transmission by random sampling. Natl. Bur. Stand. Appl. Math. Ser., 12:27-30, 1951.
  • 10. Ioannis Karatzas and Steven E. Shreve, Brownian motion and stochastic calculus, 2nd ed., Graduate Texts in Mathematics, vol. 113, Springer-Verlag, New York, 1991. MR 1121940
  • 11. Sylvie Méléard, Asymptotic behaviour of some interacting particle systems; McKean-Vlasov and Boltzmann models, Probabilistic models for nonlinear partial differential equations (Montecatini Terme, 1995) Lecture Notes in Math., vol. 1627, Springer, Berlin, 1996, pp. 42–95. MR 1431299,
  • 12. Philip E. Protter, Stochastic integration and differential equations, Stochastic Modelling and Applied Probability, vol. 21, Springer-Verlag, Berlin, 2005. Second edition. Version 2.1; Corrected third printing. MR 2273672
  • 13. Daniel Revuz and Marc Yor, Continuous martingales and Brownian motion, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 293, Springer-Verlag, Berlin, 1991. MR 1083357
  • 14. M. N. Rosenbluth and A. W. Rosenbluth. Monte Carlo calculations of the average extension of macromolecular chains. J. Chem. Phys., 23:356-359, 1955.
  • 15. Mathias Rousset, On the control of an interacting particle estimation of Schrödinger ground states, SIAM J. Math. Anal. 38 (2006), no. 3, 824–844. MR 2262944,
  • 16. Alain-Sol Sznitman, Topics in propagation of chaos, École d’Été de Probabilités de Saint-Flour XIX—1989, Lecture Notes in Math., vol. 1464, Springer, Berlin, 1991, pp. 165–251. MR 1108185,

Review Information:

Reviewer: Pierre Del Moral
Affiliation: INRIA Bordeaux-Sud Ouest Center; The Mathematical Institute of Bordeaux
Journal: Bull. Amer. Math. Soc. 48 (2011), 293-305
MSC (2010): Primary 60G35, 93E11
Published electronically: October 26, 2010
Review copyright: © Copyright 2010 American Mathematical Society