Gaussian approximation for functionals of Gibbs particle processes

Daniela Flimmel; Viktor Beneš

Kybernetika (2018)

  • Volume: 54, Issue: 4, page 765-777
  • ISSN: 0023-5954

Abstract

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In the paper asymptotic properties of functionals of stationary Gibbs particle processes are derived. Two known techniques from the point process theory in the Euclidean space ℝ d are extended to the space of compact sets on ℝ d equipped with the Hausdorff metric. First, conditions for the existence of the stationary Gibbs point process with given conditional intensity have been simplified recently. Secondly, the Malliavin-Stein method was applied to the estimation of Wasserstein distance between the Gibbs input and standard Gaussian distribution. We transform these theories to the space of compact sets and use them to derive a Gaussian approximation for functionals of a planar Gibbs segment process.

How to cite

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Flimmel, Daniela, and Beneš, Viktor. "Gaussian approximation for functionals of Gibbs particle processes." Kybernetika 54.4 (2018): 765-777. <http://eudml.org/doc/294627>.

@article{Flimmel2018,
abstract = {In the paper asymptotic properties of functionals of stationary Gibbs particle processes are derived. Two known techniques from the point process theory in the Euclidean space $\mathbb \{R\}^d$ are extended to the space of compact sets on $\mathbb \{R\}^d$ equipped with the Hausdorff metric. First, conditions for the existence of the stationary Gibbs point process with given conditional intensity have been simplified recently. Secondly, the Malliavin-Stein method was applied to the estimation of Wasserstein distance between the Gibbs input and standard Gaussian distribution. We transform these theories to the space of compact sets and use them to derive a Gaussian approximation for functionals of a planar Gibbs segment process.},
author = {Flimmel, Daniela, Beneš, Viktor},
journal = {Kybernetika},
keywords = {asymptotics of functionals; innovation; stationary Gibbs particle process; Wasserstein distance},
language = {eng},
number = {4},
pages = {765-777},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Gaussian approximation for functionals of Gibbs particle processes},
url = {http://eudml.org/doc/294627},
volume = {54},
year = {2018},
}

TY - JOUR
AU - Flimmel, Daniela
AU - Beneš, Viktor
TI - Gaussian approximation for functionals of Gibbs particle processes
JO - Kybernetika
PY - 2018
PB - Institute of Information Theory and Automation AS CR
VL - 54
IS - 4
SP - 765
EP - 777
AB - In the paper asymptotic properties of functionals of stationary Gibbs particle processes are derived. Two known techniques from the point process theory in the Euclidean space $\mathbb {R}^d$ are extended to the space of compact sets on $\mathbb {R}^d$ equipped with the Hausdorff metric. First, conditions for the existence of the stationary Gibbs point process with given conditional intensity have been simplified recently. Secondly, the Malliavin-Stein method was applied to the estimation of Wasserstein distance between the Gibbs input and standard Gaussian distribution. We transform these theories to the space of compact sets and use them to derive a Gaussian approximation for functionals of a planar Gibbs segment process.
LA - eng
KW - asymptotics of functionals; innovation; stationary Gibbs particle process; Wasserstein distance
UR - http://eudml.org/doc/294627
ER -

References

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