Random fields and the geometry of Wiener space
(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:
https://lup.lub.lu.se/record/8a83133b-5d11-4bde-9347-971a9cc4d552
- author
- Vadlamani, Sreekar LU and Taylor, Jonathan
- publishing date
- 2013
- 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
- 2022-02-14 21:38:21
@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}}, keywords = {{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}}, doi = {{10.1214/11-AOP730}}, volume = {{41}}, year = {{2013}}, }