Dynamical origin of memory and renewal


Cakir R., Grıgolını P., Krokhın A. A.

PHYSICAL REVIEW E, vol.74, 2006 (Peer-Reviewed Journal) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 74
  • Publication Date: 2006
  • Doi Number: 10.1103/physreve.74.021108
  • Journal Name: PHYSICAL REVIEW E
  • Journal Indexes: Science Citation Index Expanded, Scopus

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 Levy (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 Levy process with 0