TIME CHARACTERISTICS OF WANDERING THROUGH A SEMI-MARKOV PROCESS
The problem of time characteristics applied calculation when wandering through semi-Markov process is investigated. It is shown, that applied calculation may be reduced to solving of two tasks: evaluation of time interval of wandering from one state to another, and evaluation of time interval of return to the state. Dependencies for solving of tasks, including densities-to-characteristic functions transform, exponentiation of characteristic function, ma- trix element selection and inverse characteristic function-to-density transform, are obtained It is shown, that dependencies mentioned are to complex for practical application. Formulae for direct calculation of expectations and dispersions with use of formulated operation of nu- merical characteristics convolution are obtained. It is shown, that in this case numerical characteristics calculation is too complicated. The algorithm and mathematical expressions system for recurrent simplification of semi-Markov process, which permits to reduce compu- tational complexity of analysis, is proposed.