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Book Review

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Book Information:

Authors: Ivan Nourdin and Giovanni Peccati
Title: Normal approximations with Malliavin calculus. From Stein’s method to universality
Additional book information: Cambridge Tracts in Mathematics, Vol. 192, 2012, xii+239 pp., ISBN 978-1-107-01777-1, US $80.00

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

  • [1] Paul Malliavin, Stochastic calculus of variation and hypoelliptic operators, Equations (Res. Inst. Math. Sci., Kyoto Univ., Kyoto, 1976) Wiley, New York, 1978, pp. 195-263. MR 536013 (81f:60083)
  • [2] Paul Malliavin, Stochastic analysis, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 313, Springer-Verlag, Berlin, 1997. MR 1450093 (99b:60073)
  • [3] Elchanan Mossel, Ryan O'Donnell, and Krzysztof Oleszkiewicz, Noise stability of functions with low influences: invariance and optimality, Ann. of Math. (2) 171 (2010), no. 1, 295-341. MR 2630040 (2012a:60091), https://doi.org/10.4007/annals.2010.171.295
  • [4] Ivan Nourdin and Frederi G. Viens, Density formula and concentration inequalities with Malliavin calculus, Electron. J. Probab. 14 (2009), no. 78, 2287-2309. MR 2556018 (2011a:60147), https://doi.org/10.1214/EJP.v14-707
  • [5] David Nualart, The Malliavin calculus and related topics, 2nd ed., Probability and its Applications (New York), Springer-Verlag, Berlin, 2006. MR 2200233 (2006j:60004)
  • [6] David Nualart and Giovanni Peccati, Central limit theorems for sequences of multiple stochastic integrals, Ann. Probab. 33 (2005), no. 1, 177-193. MR 2118863 (2005k:60077), https://doi.org/10.1214/009117904000000621
  • [7] Charles Stein, Approximate computation of expectations, Institute of Mathematical Statistics Lecture Notes--Monograph Series, 7, Institute of Mathematical Statistics, Hayward, CA, 1986. MR 882007 (88j:60055)

Review Information:

Reviewer: David Nualart
Affiliation: Kansas University
Email: nualart@math.ku.edu
Journal: Bull. Amer. Math. Soc. 51 (2014), 491-497
DOI: https://doi.org/10.1090/S0273-0979-2013-01432-0
Published electronically: September 20, 2013
Review copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
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