The price time series of the Italian government bonds (BTP) futures is studied by means of scaling concepts originally developed for random walks in statistical physics. The series of overnight price differences is mapped onto a one-dimensional random walk: the bond walk. The analysis of the...

We study the scaling behavior in currency exchange rates. Our results suggest that they satisfy scaling with an exponent close to 0.5, but that it differs qualitatively from that of a simple random walk. Indeed price variations cannot be considered as independent variables and subtle...

We consider the question of when a random walk on a finite abelian group with a given step distribution can be used to reconstruct a binary labeling of the elements of the group, up to a shift. Matzinger and Lember (2006) give a sufficient condition for reconstructability on cycles. While, as we...

We consider a lattice model of the annihilation process A+B→B, when a mobile prey A is chased by identical, independent predators B performing random motions until one of them finds A and destroys it. It is assumed that each predator follows some “most probable” trajectory around which it...

The names of Grünwald and Letnikov are associated with discrete convolutions of mesh h, multiplied by h−α. When h tends to zero, the result tends to a Marchaud’s derivative (of the order of α) of the function to which the convolution is applied. The weights wkα of such discrete...

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,...

We propose a variety of models of random walk, discrete in space and time, suitable for simulating stable random variables of arbitrary index α (0α⩽2), in the symmetric case. We show that by properly scaled transition to vanishing space and time steps our random walk models converge to the...

We model the time series of the S&P500 index by a combined process, the AR+GARCH process, where AR denotes the autoregressive process which we use to account for the short-range correlations in the index changes and GARCH denotes the generalized autoregressive conditional heteroskedastic process...

We show how effectively the diffusive capture processes (DCP) on complex networks can be applied to information search in the networks. Numerical simulations show that our method generates only 2% of traffic compared with the most popular flooding-based query-packet-forwarding (FB) algorithm. We...

The one-dimensional random walk (RW), where steps up and down are performed according to the occurrence of special primes, is defined. Some quantities characterizing RW are investigated. The mean fluctuation function F(l) displays perfect power-law dependence F(l)∼l1/2 indicating that the...