Apparent multifractality of self-similar L\'evy processes

Scaling properties of time series are usually studied in terms of the scaling laws of empirical moments, which are the time average estimates of moments of the dynamic variable. Nonlinearities in the scaling function of empirical moments are generally regarded as a sign of multifractality in the data. We show that, except for the Brownian motion, this method fails to disclose the correct monofractal nature of self-similar L\'evy processes. We prove that for this class of processes it produces apparent multifractality characterised by a piecewise-linear scaling function with two different regimes, which match at the stability index of the considered process. This result is motivated by previous numerical evidence. It is obtained by introducing an appropriate stochastic normalisation which is able to cure empirical moments, without hiding their dependence on time, when moments they aim at estimating do not exist

Diffusion processes in demographic transitions: a prospect on using multi agent simulation to explore the role of cognitive strategies and social interactions

Multi agent simulation (MAS) is a tool that can be used to explore the dynamics of different systems. Considering that many demographic phenomena have roots in individual choice behaviour and social interactions it is important that this behaviour is being translated in agent rules. Several behaviour theories are relevant in this context, and hence there is a necessity of using a meta-theory of behaviour as a framework for the development of agent rules. The consumat approach provides a basis for such a framework, as is demonstrated with a discussion of modelling the diffusion of contraceptives. These diffusion processes are strongly influenced by social processes and cognitive strategies. Different possible research lines are discussed which might be addressed with a multi-agent approach like the consumats.