Jürg Hüsler: On the shape of high excursions of Gaussian processes and fields

We consider a Gaussian process which crosses a high threshold and investigate the path behavior above such a threshold. Typically the excursion is rather short in time. But when we condition on two exceedances above the threshold which are separated in time by a positive quantity, the excursions may be much longer. The conditions for such long excursions will be discussed and the paths of the conditioned process investigated as the threshold level tends to 1. This will be considered explicitly for Gaussian processes. We present extensions also for Gaussian fields.