| Title | Extreme values and crossings for the chi^2-process and othe functions of multidimensional Gaussian processes, with reliability applications |
| Authors | Georg Lindgren |
| Alternative Location | http://www.jstor.org/stable..., Restricted Access |
| Publication | Advances in Applied Probability |
| Year | 1980 |
| Volume | 12 |
| Issue | 3 |
| Pages | 746 - 774 |
| Document type | Article |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Publisher | Applied Probability Trust |
| Abstract English | Extreme values of non-linear functions of multivariate Gaussian processes are of considerable interest in engineering sciences dealing with the safety of structures. One then seeks the survival probability P{(X1(t),⋯ ,Xn(t))∈ S, all t∈ 0,T}, where X(t)=(X1(t),⋯ ,Xn(t)) is a stationary, multivariate Gaussian load process, and S is a safe region. In general, the asymptotic survival probability for large T-values is the most interesting quantity. By considering the point process formed by the extreme points of the vector process X(t), and proving a general Poisson convergence theorem, we obtain the asymptotic survival probability for a large class of safe regions, including those defined by the level curves of any second- (or higher-) degree polynomial in (x1,⋯ ,xn). This makes it possible to give an asymptotic theory for the so-called Hasofer-Lind reliability index, $\beta =\text{inf}_{x\not\in S}\|x\|$, i.e. the smallest distance from the origin to an unsafe point. |
| ISBN/ISSN/Other | ISSN: 00018678 |
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