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The rate of crossings of a quadratic form of an n-dimensional stationary Gaussian process

Hagberg, Oskar LU (2004) In Preprint without journal information
Abstract
Consider a quadratic form of a vector valued differentiable stationary Gaussian process. The crossing intensity of a fixed level depends on the joint correlation structure of the process and its derivative, but no simple exact form is known for the general case. We give the first and second terms in an asymptotic expansion, which is valid as the level tends to infinity, and show how to find higher order terms.

As a by-product of the proof we see that the crossing intensity can be written as an integral which, even if it cannot be solved by a simple formula, is easily evaluated by Monte Carlo integration. We give a simulation scheme to describe the steps in this procedure.
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author
organization
publishing date
type
Contribution to journal
publication status
unpublished
subject
in
Preprint without journal information
issue
2004:17
publisher
Manne Siegbahn Institute
ISSN
0348-7911
language
English
LU publication?
yes
id
1ab98f21-53cd-4c0b-a96d-157f5559f439 (old id 928980)
date added to LUP
2008-01-14 16:05:36
date last changed
2016-04-16 07:07:34
@misc{1ab98f21-53cd-4c0b-a96d-157f5559f439,
  abstract     = {Consider a quadratic form of a vector valued differentiable stationary Gaussian process. The crossing intensity of a fixed level depends on the joint correlation structure of the process and its derivative, but no simple exact form is known for the general case. We give the first and second terms in an asymptotic expansion, which is valid as the level tends to infinity, and show how to find higher order terms. <br/><br>
As a by-product of the proof we see that the crossing intensity can be written as an integral which, even if it cannot be solved by a simple formula, is easily evaluated by Monte Carlo integration. We give a simulation scheme to describe the steps in this procedure.},
  author       = {Hagberg, Oskar},
  issn         = {0348-7911},
  language     = {eng},
  number       = {2004:17},
  publisher    = {ARRAY(0x98882f0)},
  series       = {Preprint without journal information},
  title        = {The rate of crossings of a quadratic form of an n-dimensional stationary Gaussian process},
  year         = {2004},
}