Recurrent representation for stationary Gaussian processes

In this note, recurrent representation of stationary Gaussian processes is derived from their Probability Density Functions (PDFs). On this basis, we present the method to simulate numerically Gaussian processes ill time domain by means of a digital computer. Then, in order to ensure stability of computational calculation, we introduce some approximations in which the old information in time domain is truncated; the processes obtained through the method can be called 'Truncated Recurrent processes' (TR processes). Finally, discussing the relation between the TR processes and Autoregressive (AR) processes, it is shown that the latter are identical with a part of the former.