Asymptotic behaviour of random walks with correlated temporal structure

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...

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Bibliographic Details
Published in:Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences Mathematical, physical, and engineering sciences, 2013-11, Vol.469 (2159), p.20130419-20130419
Main Authors: Magdziarz, Marcin, Szczotka, W adys aw, ebrowski, Piotr
Format: Article
Language:English
Subjects:
Asymptotic properties
Continuous-Time Random Walk
Convergence In Distribution
Correlation
Diffusion
Ergodicity Breaking
Functions (mathematics)
Kernels
Langevin Equation
Mathematical analysis
Random walk
Stable Distribution
Subdiffusion
Temporal logic
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Summary: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.
ISSN:1364-5021
1471-2946
DOI:10.1098/rspa.2013.0419