title: Dynamical origin of memory and renewal.
abstract: We show that the dynamic approach to fractional Brownian motion (FBM) establishes a link between a non-Poisson renewal process with abrupt jumps resetting to zero the system's memory and correlated dynamic processes, whose individual trajectories keep a nonvanishing memory of their past time evolution. It is well known that the recrossings of the origin by an ordinary one-dimensional diffusion trajectory generates a Lévy (and thus renewal) process of index theta = 1/2 . We prove with theoretical and numerical arguments that this is the special case of a more general condition, insofar as the recrossings produced by the dynamic FBM generates a Lévy process with 0 < theta < 1. This result is extended to produce a satisfactory model for the fluorescent signal of blinking quantum dots.
authors.affiliation: Center for Nonlinear Science, University of North Texas, PO Box 311427, Denton, Texas 76203, USA.
authors.forename: R
authors.initials: R
authors.lastname: Cakir
authors.forename: P
authors.initials: P
authors.lastname: Grigolini
authors.forename: A A
authors.initials: AA
authors.lastname: Krokhin