The Annals of Probability

Limit theorems for coupled continuous time random walks

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

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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

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

First available in Project Euclid: 11 March 2004

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Zentralblatt MATH identifier

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]

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


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.

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