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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Book Review

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MathSciNet review: 2791780
Full text of review: PDF   This review is available free of charge.
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?)

  • 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, DOI 10.1007/s00440-004-0412-5
  • 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) NATO Advanced Study Inst. Ser., Ser. E: Appl. Sci., No. 25, Sijthoff & Noordhoff, Alphen aan den Rijn, 1978, pp. 721–734. MR 0529130
  • 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).
  • 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, DOI 10.1007/BFb0103798
  • 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, DOI 10.1007/978-1-4684-9393-1
  • 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).
  • 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, DOI 10.1007/978-1-4757-3437-9
  • 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, DOI 10.1002/9780470316658
  • T. E. Harris and H. Kahn. Estimation of particle transmission by random sampling. Natl. Bur. Stand. Appl. Math. Ser., 12:27-30, 1951.
  • 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, DOI 10.1007/978-1-4612-0949-2
  • 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, DOI 10.1007/BFb0093177
  • 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, DOI 10.1007/978-3-662-10061-5
  • 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, DOI 10.1007/978-3-662-21726-9
  • M. N. Rosenbluth and A. W. Rosenbluth. Monte Carlo calculations of the average extension of macromolecular chains. J. Chem. Phys., 23:356-359, 1955.
  • 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, DOI 10.1137/050640667
  • 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, DOI 10.1007/BFb0085169
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    Review Information:

    Reviewer: Pierre Del Moral
    Affiliation: INRIA Bordeaux-Sud Ouest Center; The Mathematical Institute of Bordeaux
    Email: pierre.del-moral@inria.fr
    Journal: Bull. Amer. Math. Soc. 48 (2011), 293-305
    DOI: https://doi.org/10.1090/S0273-0979-2010-01311-2
    Published electronically: October 26, 2010
    Review copyright: © Copyright 2010 American Mathematical Society