 Extremal ranks and transformation of variables for extremes of functions of multivariate Gaussian processesGeorg Lindgren Stochastic Processes and their Applications, 1984, vol. 17, issue 2, 285-312 Abstract: The exit rate from a 'safe region' plays an important role in dynamic reliability theory with multivariate random loads. For Gaussian processes the exit rate is simply calculated only for spherical or linear boundaries. However, many smooth boundaries, not of any of these types, are asymptotically spherical in variables of lower dimension, having a greater curvature in the remaining variables. As is shown in this paper, the asymptotic exit rate is then simply expressed as the exit rate from a sphere for a process of the lower dimensions, corrected by an explicit factor. The procedure circumvents the need to calculate complicated exit rate integrals for general boundaries, reducing the problem to a Gaussian probability integral for independent variables. A result of independent interest relates the tail distribution for a sum of a noncentral [chi]2-variable and a weighted sum of squares of noncentral normal variables, to the tail distribution of the [chi]2-variable only. Keywords: Extremal; theory; reliability; chi-squared; processes; maxima; safety; of; structures; quadratic; forms (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:17:y:1984:i:2:p:285-312 Ordering information: This journal article can be ordered from Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
Is your work missing from RePEc? Here is how to contribute.
Questions or problems? Check the EconPapers FAQ or send mail to .
EconPapers is hosted by the
School of Business at Örebro University.