Weak Convergence of High Level Exceedances by a Stationary Sequence,

In the paper the author considers a stationary sequence xi sub nn 1, 2 ... satisfying weak dependence restrictions. For each n the point process N sub n is defined to consist of the exceedances of a certain level u sub n i.e. the instants j for which xi sub j u sub n. It is shown that the point processes N sub n converge weakly as random elements of the natural metric space to which they belong to a Poisson process.