The evolution of the law of random processes in the analysis of dynamic systems

The paper presents a method for determining the evolution of the cumulative distribution function of random processes which are encountered in the study of dynamic systems with some uncertainties in the characterizing parameters. It is proved that these distribution functions are the solution of a partial differential equation, whose coefficients can be determined once the dynamic system has been solved, and whose numerical solution can be obtained with the finite difference method. Two simple problems are solved here both explicitly and numerically, then the obtained results are compared with each other.

Automated summary

The paper presents a method to determine the evolution of the cumulative distribution function of random processes in dynamic systems with uncertain parameters. It proves that these distribution functions are solutions of a partial differential equation, with coefficients determined after solving the dynamic system, and can be numerically solved using the finite difference method. Two simple problems are solved explicitly and numerically, and the obtained results are compared.