Distribution of absolute maximum of mean square differentiable Gaussian stationery process

Abstract

In this paper it is obtained the distribution of absolute maximum of mean square differentiable stationery Gaussian process by means of integration of the results of the second Kolmogorov equation solution. It is shown the way simplifying integration and its interrelation to integro-differential equation obtained before. The second Kolmogorov equation is solved first for the boundary conditions allowing to obtain the results in form of infinite series with coefficients obtained by means of solution of Sturm–Liouville problem and reducing to the simple expression. It is analyzed the correlation of obtained results with known before. It is carried out a comparative analysis of correlation functions and expressions for distribution of absolute maximums of mean square differentiable and single-component Markov processes. In spite of correlation function of single-component Markov process can be considered as limit expression for correlation function of mean square differentiable process, the expression for distribution of their absolute maximums are essentially different. It shows practical meaning of the results since real processes in radio engineering systems can be mean square differentiable only.