In represented article the questions of estimate of accuracy of an average integral characteristics of random process in the course of imitation modeling is considered. For the purposes of analytical treatment of initial stage of modeling a conditionally nonstationary Gaussian process is analyzed as stationary Gaussian process with boundary prehistory. A model of approximant autocorrelation function is recommended. Analytical expression for variance and mathematical expectation of average integral estimation are obtained. Statistical estimation efficiency criterion, the probability of belonging to correct parameter interval is introduced. Dependences of closeness in estimation statistics clearing interval at transient behavior are researched for various types of processes.