We present a generalized stochastic Cantor set by means of a simple cut and delete process and discuss the self-similar properties of the arising geometric structure. To increase the flexibility of the model, two free parameters, m and b, are introduced which tune the relative strength of the...

The purpose of this paper is to study the self-similar properties of discrete-time long memory processes. We apply our results to specific processes such as GARMA processes and GIGARCH processes, heteroscedastic models and the processes with switches and jumps.

Temporal scaling and infinite variance are two stylized features often seen together in times series of complex systems. We find that because of their infinite moments samples from fractional Lévy flights produce bi-linear scaling functions which may be incorrectly attributed as evidence of...

In this paper we recursively describe the Tutte polynomial of an infinite family of outerplanar, small-world and self-similar graphs. In particular, we study the Abelian Sandpile Model on these graphs and obtain the generating function of the recurrent configurations. Further, we give some exact...

We investigate if known extrinsic and intrinsic factors fully account for the complex features observed in recordings of human activity as measured from forearm motion in subjects undergoing their regular daily routine. We demonstrate that the apparently random forearm motion possesses dynamic...

The purpose of this paper is to study the self-similar properties of discrete-time long memory processes. We apply our results to specific processes such as GARMA processes and GIGARCH processes, heteroscedastic models and the processes with switches and jumps.