Book Review
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MathSciNet review:
3196797
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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 $80.00$
Paul Malliavin, Stochastic calculus of variation and hypoelliptic operators, Proceedings of the International Symposium on Stochastic Differential Equations (Res. Inst. Math. Sci., Kyoto Univ., Kyoto, 1976) Wiley, New York-Chichester-Brisbane, 1978, pp. 195–263. MR 536013
Paul Malliavin, Stochastic analysis, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 313, Springer-Verlag, Berlin, 1997. MR 1450093, DOI 10.1007/978-3-642-15074-6
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, DOI 10.4007/annals.2010.171.295
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, DOI 10.1214/EJP.v14-707
David Nualart, The Malliavin calculus and related topics, 2nd ed., Probability and its Applications (New York), Springer-Verlag, Berlin, 2006. MR 2200233
David Nualart and Giovanni Peccati, Central limit theorems for sequences of multiple stochastic integrals, Ann. Probab. 33 (2005), no. 1, 177–193. MR 2118863, DOI 10.1214/009117904000000621
Charles Stein, Approximate computation of expectations, Institute of Mathematical Statistics Lecture Notes—Monograph Series, vol. 7, Institute of Mathematical Statistics, Hayward, CA, 1986. MR 882007
- [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 0536013
- [2]
- Paul Malliavin, Stochastic analysis, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 313, Springer-Verlag, Berlin, 1997. MR 1450093
- [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, 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, 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
- [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, 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 0882007
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.
