Electronic Journal of Probability

Aging uncoupled continuous time random walk limits

Ofer Busani

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Aging is a prevalent phenomenon in physics, chemistry and many other fields. In this paper we consider the aging process of uncoupled Continuous Time Random Walk Limits (CTRWLs) which are Levy processes time changed by the inverse stable subordinator of index $0 < \alpha < 1$. We apply a recent method developed by Meerscheart and Straka of finding the finite dimensional distributions of CTRWL, to obtaining the aging process’s finite dimensional distributions, self-similarity-like property, asymptotic behavior and its Fractional Fokker-Planck equation(FFPE).

Article information

Electron. J. Probab., Volume 21 (2016), paper no. 7, 17 pp.

Received: 22 September 2015
Accepted: 9 November 2015
First available in Project Euclid: 5 February 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G50: Sums of independent random variables; random walks 60F17: Functional limit theorems; invariance principles
Secondary: 82C31: Stochastic methods (Fokker-Planck, Langevin, etc.) [See also 60H10]

Continuous time random walk fractional Fokker-Planck equation fractional diffusion

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Busani, Ofer. Aging uncoupled continuous time random walk limits. Electron. J. Probab. 21 (2016), paper no. 7, 17 pp. doi:10.1214/16-EJP3802. https://projecteuclid.org/euclid.ejp/1454682888

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