A path integral method is used to calculate the rate of intramolecular electron-vibration transitions taking into account the influence of the environment as the source of random Gaussian forces for vibrational degrees of freedom. The evaluation of the generating function for the rates of multiquantum transitions is reduced to the solution of some integral equations with the kernels dependent on the random force correlation function. For the Markovian Gaussian random process the exact expression for the generating function is obtained. The manifestation of the dynamical modulation effects of the surroundings fluctuations on tunnel and thermostimulated transitions is investigated.