Limit Theorem for High Level $a$-upcrossings by $\chi$-field

Siniša Stamatović, Biljana Stamatović

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.