Estimate of the accuracy of the compound Poisson approximation for the distribution of the number of matching patterns

Let X-1,..., X-m and Y-1,..., Y-n be two sequences of independent identically distributed random variables taking on values 1, 2,.... By means of a particular version of the Stein method we construct an estimate of the accuracy of approximation for the distribution of the number of matching patterns of outcomes X-i,..., Xi+s-1 of a given length 8 in the first sequence with the patterns of outcomes Y-j,..., Yj+s-1 in the second sequence. The approximating distribution is the distribution of the sum of Poisson number of independent random variables with geometric distribution.