Abstract
The Stein’s method, initiated in the 1970s by Charles Stein, is a procedure to estimate the rate of convergence in CLT-like theorems. It gained a new momentum in the beginning of the millennium thanks to the insights given by the Malliavin calculus.
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References
E. Azmoodeh, S. Campese, G. Poly, Fourth moment theorems for Markov diffusion generators. J. Funct. Anal. 266(4), 2341–2359 (2014)
E. Azmoodeh, G. Peccati, X. Yang, Malliavin–Stein method: a survey of some recent developments. Mod. Stoch. Theory Appl. 8, 141–177 (2021)
A.D. Barbour, L.H.Y. Chen, An Introduction to Stein’s Method. Lecture Notes Series, vol. 4 (National University of Singapore, Singapore, 2005)
N. Bouleau, F. Hirsch, Dirichlet Forms and Analysis on Wiener Space, vol. 14 (Walter de Gruyter & Co., Berlin, 1991)
D.J. Daley, D. Vere-Jones, An Introduction to the Theory of Point Processes. Vol. II. Springer Series in Statistics (Springer, New York, 1988)
R.M. Dudley, Distances of probability measures and random variables. Ann. Math. Stat. 39(5), 1563–1572 (1968)
R.M. Dudley, Real Analysis and Probability, vol. 74 (Cambridge University Press, Cambridge, 2002)
I. Nourdin, G. Peccati, Normal Approximations with Malliavin Calculus: From Stein’s Method to Universality. (Cambridge University Press, Cambridge, 2012)
H.-H. Shih, On Stein’s method for infinite-dimensional Gaussian approximation in abstract Wiener spaces. J. Funct. Analy. 261(5), 1236–1283 (2011)
C. Villani, Topics in Optimal Transportation. Graduate Studies in Mathematics, vol. 58. (American Mathematical Society, Providence, 2003)
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Decreusefond, L. (2022). The Malliavin–Stein Method. In: Selected Topics in Malliavin Calculus. Bocconi & Springer Series, vol 10. Springer, Cham. https://doi.org/10.1007/978-3-031-01311-9_6
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DOI: https://doi.org/10.1007/978-3-031-01311-9_6
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