Asymptotic Distributions of Characteristics of High-Level Overshoots of a Homogeneous Gaussian Random Field

1988 ◽  
Vol 32 (4) ◽  
pp. 659-669 ◽  
Author(s):  
V. P. Nosko
Keyword(s):  
Random Field ◽  
Gaussian Random Field ◽  
Asymptotic Distributions ◽  
High Level

Model fields in crossing theory: a weak convergence perspective

1988 ◽  
Vol 20 (4) ◽  
pp. 756-774
Author(s):  
Richard J. Wilson
Keyword(s):  
Weak Convergence ◽  
Random Field ◽  
Lebesgue Measure ◽  
Gaussian Random Field ◽  
Asymptotic Distributions ◽  
Asymptotic Results ◽  
Model Field ◽  
Fixed Level ◽  
Excursion Set ◽  
Crossing Theory

In this paper, the behavior of a Gaussian random field near an ‘upcrossing' of a fixed level is investigated by strengthening the results of Wilson and Adler (1982) to full weak convergence in the space of functions which have continuous derivatives up to order 2. In Section 1, weak convergence and model processes are briefly discussed. The model field of Wilson and Adler (1982) is constructed in Section 2 using full weak convergence. Some of its properties are also investigated. Section 3 contains asymptotic results for the model field, including the asymptotic distributions of the Lebesgue measure of a particular excursion set and the maximum of the model field as the level becomes arbitrarily high.

The structure of Gaussian fields near a level crossing

1982 ◽  
Vol 14 (03) ◽  
pp. 543-565 ◽  
Author(s):  
Richard J. Wilson ◽  
Robert J. Adler
Keyword(s):  
Random Field ◽  
Random Fields ◽  
Final Section ◽  
Gaussian Random Field ◽  
Asymptotic Distributions ◽  
Gaussian Fields ◽  
Level Crossing ◽  
Model Field ◽  
Definition Of

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.

Model fields in crossing theory: a weak convergence perspective

1988 ◽  
Vol 20 (04) ◽  
pp. 756-774
Author(s):  
Richard J. Wilson
Keyword(s):  
Weak Convergence ◽  
Random Field ◽  
Lebesgue Measure ◽  
Gaussian Random Field ◽  
Asymptotic Distributions ◽  
Asymptotic Results ◽  
Model Field ◽  
Fixed Level ◽  
Excursion Set ◽  
Crossing Theory

In this paper, the behavior of a Gaussian random field near an ‘upcrossing' of a fixed level is investigated by strengthening the results of Wilson and Adler (1982) to full weak convergence in the space of functions which have continuous derivatives up to order 2. In Section 1, weak convergence and model processes are briefly discussed. The model field of Wilson and Adler (1982) is constructed in Section 2 using full weak convergence. Some of its properties are also investigated. Section 3 contains asymptotic results for the model field, including the asymptotic distributions of the Lebesgue measure of a particular excursion set and the maximum of the model field as the level becomes arbitrarily high.

The structure of Gaussian fields near a level crossing

1982 ◽  
Vol 14 (3) ◽  
pp. 543-565 ◽  
Author(s):  
Richard J. Wilson ◽  
Robert J. Adler
Keyword(s):  
Random Field ◽  
Random Fields ◽  
Final Section ◽  
Gaussian Random Field ◽  
Asymptotic Distributions ◽  
Gaussian Fields ◽  
Level Crossing ◽  
Model Field ◽  
Definition Of

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.

scholarly journals ULTRAMETRIC RANDOM FIELD

2006 ◽  
Vol 09 (02) ◽  
pp. 199-213 ◽  
Author(s):  
A. YU. KHRENNIKOV ◽  
S. V. KOZYREV
Keyword(s):  
Wavelet Analysis ◽  
Random Field ◽  
Stochastic Equation ◽  
Gaussian Random Field ◽  
Ultrametric Space ◽  
Ultrametric Spaces

Gaussian random field on general ultrametric space is introduced as a solution of pseudodifferential stochastic equation. Covariation of the introduced random field is computed with the help of wavelet analysis on ultrametric spaces. Notion of ultrametric Markovianity, which describes independence of contributions to random field from different ultrametric balls is introduced. We show that the random field under investigation satisfies this property.

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