The horizon problem for random surfaces

1991 ◽  
Vol 109 (1) ◽  
pp. 211-219 ◽  
Author(s):  
K. J. Falconer
Keyword(s):  
Computer Simulation ◽  
Stochastic Processes ◽  
Random Field ◽  
Random Fields ◽  
Sample Function ◽  
Gaussian Fields ◽  
Random Surfaces ◽  
Horizon Problem ◽  
Typical Sample

Computer simulation of landscapes and skylines has recently attracted a great deal of interest: see [6, 7]. Specification of a ‘landscape’ requires a function f: D → ℝ on a subset D of ℝ2, selected so that the apparent irregularity and randomness of the surface {(t,f(t)): t ∈ D} corresponds to what might be observed in nature. It is natural to look to random fields (that is, stochastic processes in two variables), and in particular to Gaussian fields, for functions with such properties. Even when an appropriate random field has been selected, determination of a typical sample function is far from easy [7].

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.

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 Determination of Left Ventricular End Diastolic Pressure Utilizing Non-Invasive Techniques: A Computer Simulation Study

2016 ◽  
Vol 22 (8) ◽  
pp. S43-S44
Author(s):  
Ying Sun ◽  
Toby Steinberg ◽  
Jeremy Rier ◽  
Stewart Benton ◽  
Daniel Steinberg ◽  
...  
Keyword(s):  
Computer Simulation ◽  
Simulation Study ◽  
Diastolic Pressure ◽  
Left Ventricular ◽  
Computer Simulation Study ◽  
Non Invasive ◽  
Invasive Techniques

scholarly journals Stochastic Processes with a Particular Type of Variograms

2007 ◽  
Vol 2007 ◽  
pp. 1-5 ◽  
Author(s):  
Chunsheng Ma
Keyword(s):  
Stochastic Process ◽  
Brownian Motion ◽  
Stochastic Processes ◽  
Series Expansion ◽  
Real Line ◽  
Random Fields ◽  
The Other ◽  
Simple Construction ◽  
The Real ◽  
Line Form

This paper is concerned with a class of stochastic processes or random fields with second-order increments, whose variograms have a particular form, among which stochastic processes having orthogonal increments on the real line form an important subclass. A natural issue, how big this subclass is, has not been explicitly addressed in the literature. As a solution, this paper characterizes a stochastic process having orthogonal increments on the real line in terms of its variogram or its construction. Our findings are a little bit surprising: this subclass is big in terms of the variogram, and on the other hand, it is relatively “small” according to a simple construction. In particular, every such process with Gaussian increments can be simply constructed from Brownian motion. Using the characterizations we obtain a series expansion of the stochastic process with orthogonal increments.

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