The shape of trajectories of Gaussian processes having large excursions

We study the shape of excursions above a high level by a stationary Gaussian process, conditioned on whether this happens in a cluster or two clusters. In the first part of the thesis, the shape of a simple excursion is considered. It is shown that its trajectory varies slightly around a deterministic trend. In the second part, a similar result has been obtained for excursions above a high level which is based on at least two excursion points separated by a fixed positive number. We call such excursions massive excursions. The behavior of the probabilities of events generated by massive excursions depends on the location of the correlation function maximum of the process. The two possible cases of the location are considered. Proofs are performed separately for smooth and non-smooth Gaussian processes, using different approaches.