We studied random walks on two-dimensional patterns formed by the sequence of configurations of complex elementary cellular automata (CA) with random initial configurations. The walkers are allowed to jump between nearest neighbours or next nearest neighbours 1 sites. On patterns of rules 22,...

In this work we extend the recently considered toy model of Weierstrass or Lévy walks with varying velocity of the walker (Quantitative Finance 3 (2003) 201; Chem. Phys. 284 (2002) 481; Comp. Phys. Comm. 147 (2002) 565; Phys. A 264 (1999) 84; Phys. A 264 (1999) 107) by introducing a more realistic...

The paper consists of two parts: (i) the empirical one where the non-linear, long-term autocorrelations present in high-frequency data extracting from the Warsaw Stock Exchange were analyzed and (ii) theoretical one where predictions of our model (Quantitative Finance 3 (2003) 201; Physica A...