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Random fields and the geometry of Wiener space

Vadlamani, Sreekar LU and Taylor, Jonathan (2013) In Annals of Probability 41(4). p.2724-2754
Abstract
In this work we consider infinite dimensional extensions of some finite dimensional Gaussian geometric functionals called the Gaussian Minkowski functionals. These functionals appear as coefficients in the probability content of a tube around a convex set D⊂RkD⊂Rk under the standard Gaussian law N(0,Ik×k)N(0,Ik×k). Using these infinite dimensional extensions, we consider geometric properties of some smooth random fields in the spirit of [Random Fields and Geometry (2007) Springer] that can be expressed in terms of reasonably smooth Wiener functionals.
Please use this url to cite or link to this publication:
author
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Wiener space, Malliavin calculus, random fields
in
Annals of Probability
volume
41
issue
4
pages
31 pages
publisher
Institute of Mathematical Statistics
external identifiers
  • scopus:84881514518
ISSN
0091-1798
DOI
10.1214/11-AOP730
language
English
LU publication?
no
id
8a83133b-5d11-4bde-9347-971a9cc4d552
date added to LUP
2017-09-01 12:00:50
date last changed
2018-01-07 12:17:04
@article{8a83133b-5d11-4bde-9347-971a9cc4d552,
  abstract     = {In this work we consider infinite dimensional extensions of some finite dimensional Gaussian geometric functionals called the Gaussian Minkowski functionals. These functionals appear as coefficients in the probability content of a tube around a convex set D⊂RkD⊂Rk under the standard Gaussian law N(0,Ik×k)N(0,Ik×k). Using these infinite dimensional extensions, we consider geometric properties of some smooth random fields in the spirit of [Random Fields and Geometry (2007) Springer] that can be expressed in terms of reasonably smooth Wiener functionals.},
  author       = {Vadlamani, Sreekar and Taylor, Jonathan},
  issn         = {0091-1798},
  keyword      = {Wiener space,Malliavin calculus,random fields},
  language     = {eng},
  number       = {4},
  pages        = {2724--2754},
  publisher    = {Institute of Mathematical Statistics},
  series       = {Annals of Probability},
  title        = {Random fields and the geometry of Wiener space},
  url          = {http://dx.doi.org/10.1214/11-AOP730},
  volume       = {41},
  year         = {2013},
}