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We prove a Poisson limit theorem in the total variation distance of functionals of a general Poisson point process using the Malliavin-Stein method.
“Stein’s method and normal approximation of Poisson functionals”
G. Peccati, J.. Solé, M.. Taqqu and F. Utzet · 2010
Earlier work this paper cites.
“High-dimensional random geometric graphs and their clique number”
Luc Devroye, András György, Gábor Lugosi and Frederic Udina · 2011
Earlier work this paper cites.
“Poisson process Fock space representation, chaos expansion and covariance inequalities”
Günter Last and Mathew. Penrose · 2011
Earlier work this paper cites.
“The Chen-Stein method for Poisson functionals” 18 pages; some small typos, in particular in the proof of Theorem 5.1, have been corrected., 2012
Giovanni Peccati · 2012
Earlier work this paper cites.
“Gamma limits and U U -statistics on the Poisson space”
Giovanni Peccati and Christoph Thäle · 2013
Earlier work this paper cites.
“Central limit theorems for U U -statistics of Poisson point processes”
Matthias Reitzner and Matthias Schulte · 2013
Cited alongside, same era.
“The Malliavin-Stein method on the Poisson space”
Solesne Bourguin and Giovanni Peccati · 2016
Cited alongside, same era.
“Testing for high-dimensional geometry in random graphs”
Sébastien Bubeck, Jian Ding, Ronen Eldan and Miklós. Rácz · 2016
Cited alongside, same era.
“Gaussian fluctuations for edge counts in high-dimensional random geometric graphs”
Jens Grygierek and Christoph Thäle · 2016
Cited alongside, same era.
“Stochastic analysis for Poisson processes”
Günter Last · 2016
Later among the works it cites.
“Normal approximation on Poisson spaces: Mehler’s formula, second order Poincaré inequalities and stabilization”
Günter Last, Giovanni Peccati and Matthias Schulte · 2016
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Bocconi University Press, [place of publication not identified]; Springer, [Cham], 2016, pp. xv+346
“Stochastic analysis for Poisson point processes” Malliavin calculus, Wiener-Itô chaos expansions and stochastic geometry 7 · 2016
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“Lectures on the Poisson process” 7
Günter Last and Mathew Penrose · 2018
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