MATEMATIČKI VESNIK
МАТЕМАТИЧКИ ВЕСНИК



MATEMATIČKI VESNIK
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.

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Keywords: Gaussian vector field, Poisson field, $A$-points.

MSC: 60G15, 60G60

Pages:  99--108     

Volume  57 ,  Issue  3$-$4 ,  2005