The reception of electromagnetic signals depends on the polarisation matching of the transmitting and receiving antenna. The practical matching differs from the theoretical one because of the noise deterioration of the transmitted and eventually received electromagnetic field. In other applications, the polarisation parameters of the receiving antenna are not known. Both problems are addressed by means of statistical methods, analytical as well as simulation results are obtained. The variation of the noisy matching factor depends mainly on the signal-to-noise ratio. The resulting probability distribution for the polarisation matching factor in case of a stochastic receiver is independent of the phase difference, but strongly affected by the axis ratio of the incident polarised field.