Electronic Journal of Probability

Aging uncoupled continuous time random walk limits

Ofer Busani

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1454682888

Digital Object Identifier
doi:10.1214/16-EJP3802

Mathematical Reviews number (MathSciNet)
MR3485349

Zentralblatt MATH identifier
1338.60123

Subjects
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]

Keywords
Continuous time random walk fractional Fokker-Planck equation fractional diffusion

Rights
Creative Commons Attribution 4.0 International License.

Citation

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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