  We derive the stochastic Schr\"odinger equation for the system wave vector
and use it to describe the excitation energy transfer dynamics in molecular
aggregates. We suggest a quantum-measurement based method of estimating the
excitation transfer time. Adequacy of the proposed approach is demonstrated by
performing calculations on a model system. The theory is then applied to study
the excitation transfer dynamics in a photosynthetic pigment-protein
Fenna-Matthews-Olson (FMO) aggregate using both the Debye spectral density and
the spectral density obtained from earlier molecular dynamics simulations
containing strong vibrational high-frequency modes. The obtained results show
that the excitation transfer times in the FMO system are affected by the
presence of the vibrational modes, however the transfer pathways remain the
same.
