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[en] The excitation of a resonance embedded in a continuum by intense radiation requires a theoretical description beyond the transition probability per unit time. This implies a time-dependent formulation incorporating all features of the radiation source, such as pulse temporal shape and duration, as well as stochastic properties, for pulses other than Fourier limited. The radiation from short wavelength free electron lasers is a case in point, as it is the only source that can provide the necessary intensity. In view of ongoing experiments with such sources, we present a systematic study for an isolated autoionizing resonance. We find that intensity, pulse duration and field fluctuations conspire in producing unexpected excitation profiles, not amenable to a description in terms of the usual Fano profile. In particular, the role of intensity fluctuations turns out to pose challenging theoretical problems part of which have been addressed herein. Graphical abstract: .