Non-poisson processes: Regression to equilibrium versus equilibrium correlation functions

Physica A: Statistical Mechanics and its Applications

Volumn 347, Issue , 2005, Pages 268-288

  Allegrini, Paolo ^a   Grigolini, Paolo ^b,c,d   Palatella, Luigi ^e   Rosa, Angelo ^f   West, Bruce J ^g  

^a INFM   (Italy)

^b UNIVERSITY OF NORTH TEXAS   (United States)

^c UNIVERSITY OF PISA   (Italy)

^d CNR   (Italy)

^e UNIVERSITÀ DI ROMA LA SAPIENZA   (Italy)

^f EPFL   (Switzerland)

^g U S ARMY RESEARCH OFFICE   (United States)

Author keywords

Correlation function; Liouville and Liouville like equations; Non Poisson processes; Regression to equilibrium; Stochastic processes

Indexed keywords

CORRELATION THEORY; DIFFUSION; INTEGRATION; PHASE EQUILIBRIA; POISSON EQUATION; QUANTUM THEORY; REGRESSION ANALYSIS;

CORRELATION FUNCTIONS; LIOUVILLE AND LIOUVILLE-LIKE EQUATIONS; NON-POISSON PROCESSES; REGRESSION TO EQUILIBRIUM;

RANDOM PROCESSES;

EID: 10644254270     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2004.08.004     Document Type: Article

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28. In the case where the renewal condition applies, we want to point out that, as shown in (1), the GME can be derived from the CTRW [3]. It is still unknown how to do that using the Liouville-like approach of Section 2, probably due to the complexity of the problem illustrated in Section 6. Furthermore, the authors of Ref. [12] made the following impressive discovery. In the non-Poisson case even if a correct GME is available [29], its response to external perturbations departs from the correct prediction that one can obtain by perturbing the CTRW instead. Thus the trajectory-density conflict [16] seems to be the manifestation of technical problems, emerging from the density perspective, which can be settled using the trajectory (CTRW) perspective.
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