Sampling procedure of the arithmetic operations with two Binary Markov Process realizations

The sampling procedure of the arithmetic operation with two Binary Markov Processes (BMP) is considered in detail, especially for the sum of BMP. The result of the sum can have four or three states. In the first case there is a Markovian process, in the second case the process is non Markovian. We investigate sampling procedure of any realization of this case. The investigation method takes into account the probability of the state omission and probability densities functions of staying times in each state. We obtain the algorithm for choosing of sampling intervals for each state. They are different. One non trivial example is given. The obtained results are generalized for other arithmetic operations: the multiplication and division. One rather important variant of the application of such processes in the random field model is given at the final paragraph.