Lévy processes, subordinators and crime modelling

Tijana Levajković, Hermann Mena, Martin Zarfl

We investigate some properties of Lévy processes in the context of subordinators. Lévy walks can be represented as subordinators of random walks and Lévy flights are random walks with trajectories composed of self-similar jumps. Lévy processes provide a framework for modelling many physical phenomena. In this paper we consider, as an illustration, crime models based on Brownian motion and Lévy flights. We propose an efficient implementation of the models by using high performance computing techniques. Numerical simulations on different scenarios allows us to analyze some properties of the processes, particularly regimes of aggregation and first passage time.