An analytic technique recently developed for solving the nonlocal Markov equation for the mean field is further extended for treating the equation for the spaced position coherence function of the random field. The model rigorous explicit solution is presented for this function, which takes account of the finite values of the longitudinal correlation radius of fluctuations. It is also discussed how this theory can be employed for further modernization of the earlier developed simulators of the stochastic signals of very high frequencies, propagating through fluctuating plasma.