The process of resonant tunnelling of electrons through the double-barrier nanostructure under the influence of external noises caused by the amplitude and phase fluctuations in an incoming current is considered. With the account of electrostatic repulsion in a quantum well, the regime of tunnelling at specified parameter values becomes bistable and possesses heightened sensibility to noises at instability points. Noise is taken as a Gaussian process with zero correlation time. The influence of noises on a stationary correlation function of the intensity of an outgoing electron flow is investigated at two branches of a hysteresis cycle and in the vicinity of an unstable point. For the calculation of the correlation function, a method of linearization in the neighbourhood of an unperturbed dynamical regime is used. The results are compared with those obtained by numerical simulation of stochastic evolution equations. As shown, the amplitude and phase fluctuations have effects on the correlation-function form in a different way. With the growth of the intensity of the amplitude noise, the square under the correlation-function curve is increased that is the evidence of the relaxation time growth. On the contrary, with increasing of the phase noise, it is decreased. A satisfactory agreement of numerical results with analytical calculations at the decay of the correlation function is achieved.