| Limit theorem for high level $A$-upcrossings by $\chi$-field |
| Siniša Stamatović and Biljana Stamatović |
Abstract A Poisson limit theorem for $A$-points of upcrossings of a high level by trajectories of the random field $\chi(t)$ is established. Kallenberg theorem, standard results from asymptotic methods of Gaussian process and fields and Piterbarg result of high level intersection of $\chi$-field are exploited.
|
Keywords: Gaussian vector field, Poisson field, $A$-points. |
MSC: 60G15, 60G60 |
Pages: 99$-$108 |
Volume 57 , Issue 3$-$4 , 2005 |
