ABSTRACT
This chapter considers a domain of possible values of the mathematical expectation as a function of the mathematical expectation estimate. Thus, in the case of the limited a priori domain of possible values of the mathematical expectation of stochastic process, the maximum likelihood estimate of the stochastic process mathematical expectation is conditionally biased. Determine the unconditional bias and dispersion of maximum likelihood estimate of stochastic process mathematical expectation in the case of the limited a priori domain of possible estimate values. Optimal methods to estimate the stochastic process mathematical expectation envisage the need for having accurate and complete knowledge of other statistical characteristics of the considered stochastic process. Presence of limitations leads to additional errors while measuring the mathematical expectation of stochastic process. The weight coefficients are chosen from the condition of minimization of the variance of mathematical expectation estimate. Define an effect of stochastic process quantization by amplitude on the estimate of its mathematical expectation.
