Memory Functions of the Additive Markov chains: Applications to Complex   Dynamic Systems
  A new approach to describing correlation properties of complex dynamic systems with long-range memory based on a concept of additive Markov chains (Phys. Rev. E 68, 061107 (2003)) is developed. An equation connecting a memory function of the chain and its correlation function is presented. This equation allows reconstructing the memory function using the correlation function of the system. Thus, we have elaborated a novel method to generate a sequence with prescribed correlation function. Effectiveness and robustness of the proposed method is demonstrated by simple model examples. Memory functions of concrete coarse-grained literary texts are found and their universal power-law behavior at long distances is revealed. 
S. S. Melnyk, O. V. Usatenko, and V. A. Yampol'skii