title: Asymptotic behaviour of random walks with correlated temporal structure.
abstract: We introduce a continuous-time random walk process with correlated temporal structure. The dependence between consecutive waiting times is generated by weighted sums of independent random variables combined with a reflecting boundary condition. The weights are determined by the memory kernel, which belongs to the broad class of regularly varying functions. We derive the corresponding diffusion limit and prove its subdiffusive character. Analysing the set of corresponding coupled Langevin equations, we verify the speed of relaxation, Einstein relations, equilibrium distributions, ageing and ergodicity breaking.
authors.affiliation: Hugo Steinhaus Center , Institute of Mathematics and Computer Science, Wrocław University of Technology , Wybrzeze Wyspianskiego 27, 50-370 Wrocław, Poland.
authors.forename: Marcin
authors.initials: M
authors.lastname: Magdziarz
authors.forename: Władysław
authors.initials: W
authors.lastname: Szczotka
authors.forename: Piotr
authors.initials: P
authors.lastname: Zebrowski
keywords: Langevin equation; continuous-time random walk; convergence in distribution; ergodicity breaking; stable distribution; subdiffusion