Sampling and reconstruction of piecewise constant stochastic processes with Erlang stay time in states

A statistical sampling and reconstruction procedure is developed for the class of stochastic processes indicated in the title. The Erlang phase method and recurrent recalculation for conditional Markov processes are used. Formulas for the a posteriori distribution of the transition time are obtained for the respective first moments and sampling interval. The procedures are easy-to-implement computationally. The influence of process parameters on the procedure parameters is analyzed. An illustrative example is given.