Correlated continuous time random walks: combining scale-invariance with long-range memory for spatial and temporal dynamics (Q2873624)

The paper introduces and describes the properties of a complex stochastic process, namely the correlated continuous time random walk (CCTRW). This new stochastic model, which seems to be very well motivated by recent physical experiments, extends some classical processes as the continuous time random walk (CTRW), the fractional Brownian motion (FBM) and the Lévy flights. In the proposed construction, a correlation method of a Gaussian random walk (based on linear transformations) is transferred to a time-continuous process. In the last step of the definition of the CCTRW model, the correlations of waiting times are introduced.NEWLINENEWLINEThe detailed description of this very general model includes the comparison with a series of some well-known processes, the highlighting of its asymptotic stationarity, the study of the single-time probability density functions and the time scaling analysis. Sample trajectories of such processes are illustrated and commented.NEWLINENEWLINEThe authors conclude that this model is applicable to a wide range of complex systems.