2010
DOI: 10.1214/ejp.v15-823
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Stein's Method and Stochastic Analysis of Rademacher Functionals

Abstract: We compute explicit bounds in the Gaussian approximation of functionals of infinite Rademacher sequences. Our tools involve Stein's method, as well as the use of appropriate discrete Malliavin operators. Although our approach does not require the classical use of exchangeable pairs, we employ a chaos expansion in order to construct an explicit exchangeable pair vector for any random variable which depends on a finite set of Rademacher variables. Among several examples, which include random variables which depe… Show more

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Cited by 25 publications
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“…Discrete-time normal martingales [8] play an important role in many theoretical and applied fields. In recent years, functionals of discrete-time normal martingales have attracted much attention ( [3,5,7,[11][12][13]).…”
Section: Introductionmentioning
confidence: 99%
“…Discrete-time normal martingales [8] play an important role in many theoretical and applied fields. In recent years, functionals of discrete-time normal martingales have attracted much attention ( [3,5,7,[11][12][13]).…”
Section: Introductionmentioning
confidence: 99%