title: Aging ballistic Lévy walks.
abstract: Aging can be observed for numerous physical systems. In such systems statistical properties [like probability distribution, mean square displacement (MSD), first-passage time] depend on a time span t_{a} between the initialization and the beginning of observations. In this paper we study aging properties of ballistic Lévy walks and two closely related jump models: wait-first and jump-first. We calculate explicitly their probability distributions and MSDs. It turns out that despite similarities these models react very differently to the delay t_{a}. Aging weakly affects the shape of probability density function and MSD of standard Lévy walks. For the jump models the shape of the probability density function is changed drastically. Moreover for the wait-first jump model we observe a different behavior of MSD when t_{a}≪t and t_{a}≫t.
authors.affiliation: Faculty of Pure and Applied Mathematics, Hugo Steinhaus Center, Wroclaw University of Science and Technology, Wyspianskiego 27, 50-370 Wroclaw, Poland.
authors.forename: Marcin
authors.initials: M
authors.lastname: Magdziarz
authors.affiliation: Faculty of Pure and Applied Mathematics, Hugo Steinhaus Center, Wroclaw University of Science and Technology, Wyspianskiego 27, 50-370 Wroclaw, Poland.
authors.forename: Tomasz
authors.initials: T
authors.lastname: Zorawik