Anomalous diffusion in non-Markovian walks having amnestically induced persistence.
We report numerically and analytically estimated values for the Hurst exponent for a recently proposed non-Markovian walk characterized by amnestically induced persistence. These results are consistent with earlier studies showing that log-periodic oscillations arise only for large memory losses of the recent past. We also report numerical estimates of the Hurst exponent for non-Markovian walks with diluted memory. Finally, we study walks with a fractal memory of the past for a Thue-Morse and Fibonacci memory patterns. These results are interpreted and discussed in the context of the necessary and sufficient conditions for the central limit theorem to hold.
Ferreira
A S
AS
Instituto de Física, Universidade Federal de Alagoas, Maceió 57072-970, AL, Brazil.
Cressoni
J C
JC
Viswanathan
G M
GM
Alves da Silva
Marco Antonio
MA