Dynamical Origin of Memory and Renewal

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This article discusses a dynamical origin of memory and renewal.

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6 p.

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Cakir, Rasit; Grigolini, Paolo & Krokhin, Arkadii A. August 8, 2006.

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This article discusses a dynamical origin of memory and renewal.

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6 p.

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Copyright 2006 American Physical Society. The following article appeared in Physical Review Letters E, 74:2; http://pre.aps.org/abstract/PRE/v74/i2/e021108

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 θ=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<θ<1. This result is extended to produce a satisfactory model for the fluorescent signal of blinking quantum dots.

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  • Physical Review E, 2006, College Park: American Physical Society

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  • Publication Title: Physical Review E
  • Volume: 74
  • Issue: 2
  • Peer Reviewed: Yes

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UNT Scholarly Works

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  • August 8, 2006

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  • Sept. 9, 2011, 2:01 p.m.

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  • March 27, 2014, 4:19 p.m.

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Cakir, Rasit; Grigolini, Paolo & Krokhin, Arkadii A. Dynamical Origin of Memory and Renewal, article, August 8, 2006; [College Park, Maryland]. (digital.library.unt.edu/ark:/67531/metadc40399/: accessed December 12, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT College of Arts and Sciences.