DOI: 10.2307/1426673. The structure of Gaussian fields near a level crossing

The structure of Gaussian fields near a level crossing

10.2307/1426673

Crossref journal-article

Cambridge University Press (CUP)

Advances in Applied Probability (56)

Abstract

In this paper, we investigate the behaviour of a Gaussian random field after an ‘upcrossing' of a particular level. In Section 1, we briefly discuss model processes and their background, and give a definition of an upcrossing of a level for random fields. A model field is constructed for the random field after an upcrossing of a level by using horizontal window conditioning in Section 2. The final section contains asymptotic distributions for the model field and for the location and height of the ‘closest' maximum to the upcrossing as the level becomes arbitrarily high.

Bibliography

Wilson, R. J., & Adler, R. J. (1982). The structure of Gaussian fields near a level crossing. Advances in Applied Probability, 14(3), 543â565.

Authors 2

Richard J. Wilson (first)
Robert J. Adler (additional)

References 13 Referenced 20

10.1016/0304-4149(77)90025-4
10.1007/BF02384809
{'key': 'S0001867800020632_ref13', 'volume-title': 'Time Series Analysis', 'author': 'Slepian', 'year': '1962'} / Time Series Analysis by Slepian (1962)
10.1017/S0001867800042920
10.1137/1114036
{'key': 'S0001867800020632_ref3', 'volume-title': 'The Geometry of Random Fields.', 'author': 'Adler', 'year': '1981'} / The Geometry of Random Fields. by Adler (1981)
{'key': 'S0001867800020632_ref5', 'first-page': '1107', 'article-title': 'Bursts and shines of random fields', 'volume': '8', 'author': 'Belyaev', 'year': '1967', 'journal-title': 'Soviet Math. Dokl.'} / Soviet Math. Dokl. / Bursts and shines of random fields by Belyaev (1967)
10.1214/aoms/1177706105
10.1016/0304-4149(77)90046-1
{'key': 'S0001867800020632_ref7', 'volume-title': 'A Course in Probability Theory', 'author': 'Chung', 'year': '1974'} / A Course in Probability Theory by Chung (1974)
{'key': 'S0001867800020632_ref4', 'volume-title': 'Mathematical Analysis.', 'author': 'Apostol', 'year': '1957'} / Mathematical Analysis. by Apostol (1957)
10.1214/aoms/1177696688
10.1214/aop/1176996349

Dates

Type	When
Created	19 years, 4 months ago (April 23, 2006, 7:46 p.m.)
Deposited	6 years, 3 months ago (May 24, 2019, 4:40 p.m.)
Indexed	1 year ago (Aug. 5, 2024, 3:54 p.m.)
Issued	43 years ago (Sept. 1, 1982)
Published	43 years ago (Sept. 1, 1982)
Published Online	9 years, 2 months ago (July 1, 2016)
Published Print	43 years ago (Sept. 1, 1982)

Funders 0

None

BibTeX

@article{Wilson_1982, title={The structure of Gaussian fields near a level crossing}, volume={14}, ISSN={1475-6064}, url={http://dx.doi.org/10.2307/1426673}, DOI={10.2307/1426673}, number={3}, journal={Advances in Applied Probability}, publisher={Cambridge University Press (CUP)}, author={Wilson, Richard J. and Adler, Robert J.}, year={1982}, month=sep, pages={543–565} }

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