We will not detail here the structure of the corresponding sparse transition matrix ∏ (see [13]) but we need to know its number ζ of non zero terms. If a is an integer value (we suppose here that the scale factor has been already included in it) then the order of R is M × a × η and ζ = O(M × a × η2) (and we get O(M × a × ηm+1) when an order m Markov model is considered).