## The Annals of Probability

### Limit theorems for coupled continuous time random walks

#### 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

https://projecteuclid.org/euclid.aop/1079021462

Digital Object Identifier
doi:10.1214/aop/1079021462

Mathematical Reviews number (MathSciNet)
MR2039941

Zentralblatt MATH identifier
1054.60052

#### 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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