The Annals of Probability

Limit theorems for coupled continuous time random walks

Peter Becker-Kern, Mark M. Meerschaert, and Hans-Peter Scheffler

Full-text: Open access

Abstract

Scaling limits of continuous time random walks are used in physics to model anomalous diffusion, in which a cloud of particles spreads at a different rate than the classical Brownian motion. Governing equations for these limit processes generalize the classical diffusion equation. In this article, we characterize scaling limits in the case where the particle jump sizes and the waiting time between jumps are dependent. This leads to an efficient method of computing the limit, and a surprising connection to fractional derivatives.

Article information

Source
Ann. Probab., Volume 32, Number 1B (2004), 730-756.

Dates
First available in Project Euclid: 11 March 2004

Permanent link to this document
https://projecteuclid.org/euclid.aop/1079021462

Digital Object Identifier
doi:10.1214/aop/1079021462

Mathematical Reviews number (MathSciNet)
MR2039941

Zentralblatt MATH identifier
1054.60052

Subjects
Primary: 60G50: Sums of independent random variables; random walks 60F17: Functional limit theorems; invariance principles
Secondary: 60H30: Applications of stochastic analysis (to PDE, etc.) 82C31: Stochastic methods (Fokker-Planck, Langevin, etc.) [See also 60H10]

Keywords
Continuous time random walk functional limit theorem fractional derivative operator stable law

Citation

Becker-Kern, Peter; Meerschaert, Mark M.; Scheffler, Hans-Peter. Limit theorems for coupled continuous time random walks. Ann. Probab. 32 (2004), no. 1B, 730--756. doi:10.1214/aop/1079021462. https://projecteuclid.org/euclid.aop/1079021462


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