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Central Limit Theorem for Lipschitz-Killing curvatures of excursion sets Gaussian fields

Vadlamani, Sreekar LU and Kratz, Marie (2017) In Journal of Theoretical Probability
Abstract
Our interest in this paper is to explore limit theorems for various geometric functionals of excursion sets of isotropic Gaussian random fields. In the past, asymptotics of nonlinear functionals of Gaussian random fields have been studied [see Berman (Sojourns and extremes of stochastic processes, Wadsworth & Brooks, Monterey, 1991), Kratz and León (Extremes 3(1):57–86, 2000), Kratz and León (J Theor Probab 14(3):639–672, 2001), Meshenmoser and Shashkin (Stat Probab Lett 81(6):642–646, 2011), Pham (Stoch Proc Appl 123(6):2158–2174, 2013), Spodarev (Chapter in modern stochastics and applications, volume 90 of the series Springer optimization and its applications, pp 221–241, 2013) for a sample of works in such settings], the most recent... (More)
Our interest in this paper is to explore limit theorems for various geometric functionals of excursion sets of isotropic Gaussian random fields. In the past, asymptotics of nonlinear functionals of Gaussian random fields have been studied [see Berman (Sojourns and extremes of stochastic processes, Wadsworth & Brooks, Monterey, 1991), Kratz and León (Extremes 3(1):57–86, 2000), Kratz and León (J Theor Probab 14(3):639–672, 2001), Meshenmoser and Shashkin (Stat Probab Lett 81(6):642–646, 2011), Pham (Stoch Proc Appl 123(6):2158–2174, 2013), Spodarev (Chapter in modern stochastics and applications, volume 90 of the series Springer optimization and its applications, pp 221–241, 2013) for a sample of works in such settings], the most recent addition being (Adler and Naitzat in Stoch Proc Appl 2016; Estrade and León in Ann Probab 2016) where a central limit theorem (CLT) for Euler integral and Euler–Poincaré characteristic, respectively, of the excursions set of a Gaussian random field is proven under some conditions. In this paper, we obtain a CLT for some global geometric functionals, called the Lipschitz–Killing curvatures of excursion sets of Gaussian random fields, in an appropriate setting. (Less)
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author
publishing date
type
Contribution to journal
publication status
epub
subject
keywords
chaos expansion, central Limit Theorem, excursion sets, Gaussian fields, Lipschitz-Killing curvatures, 60F05, 60G15, 60G60, 60G10, 60D05, 53C65, 14M15
in
Journal of Theoretical Probability
pages
30 pages
publisher
Kluwer
external identifiers
  • scopus:85016907322
ISSN
1572-9230
DOI
10.1007/s10959-017-0760-6
language
English
LU publication?
no
id
2bd9c8eb-1b79-40be-9e50-7136544e333e
date added to LUP
2017-09-01 11:49:33
date last changed
2018-01-07 12:17:04
@article{2bd9c8eb-1b79-40be-9e50-7136544e333e,
  abstract     = {Our interest in this paper is to explore limit theorems for various geometric functionals of excursion sets of isotropic Gaussian random fields. In the past, asymptotics of nonlinear functionals of Gaussian random fields have been studied [see Berman (Sojourns and extremes of stochastic processes, Wadsworth & Brooks, Monterey, 1991), Kratz and León (Extremes 3(1):57–86, 2000), Kratz and León (J Theor Probab 14(3):639–672, 2001), Meshenmoser and Shashkin (Stat Probab Lett 81(6):642–646, 2011), Pham (Stoch Proc Appl 123(6):2158–2174, 2013), Spodarev (Chapter in modern stochastics and applications, volume 90 of the series Springer optimization and its applications, pp 221–241, 2013) for a sample of works in such settings], the most recent addition being (Adler and Naitzat in Stoch Proc Appl 2016; Estrade and León in Ann Probab 2016) where a central limit theorem (CLT) for Euler integral and Euler–Poincaré characteristic, respectively, of the excursions set of a Gaussian random field is proven under some conditions. In this paper, we obtain a CLT for some global geometric functionals, called the Lipschitz–Killing curvatures of excursion sets of Gaussian random fields, in an appropriate setting.},
  author       = {Vadlamani, Sreekar and Kratz, Marie},
  issn         = {1572-9230},
  keyword      = {chaos expansion,central Limit Theorem,excursion sets,Gaussian fields,Lipschitz-Killing curvatures,60F05,60G15,60G60,60G10,60D05,53C65,14M15 },
  language     = {eng},
  pages        = {30},
  publisher    = {Kluwer},
  series       = {Journal of Theoretical Probability},
  title        = {Central Limit Theorem for Lipschitz-Killing curvatures of excursion sets Gaussian fields},
  url          = {http://dx.doi.org/10.1007/s10959-017-0760-6},
  year         = {2017},
}