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January 2004 Limit theorems for coupled continuous time random walks
Peter Becker-Kern, Mark M. Meerschaert, Hans-Peter Scheffler
Ann. Probab. 32(1B): 730-756 (January 2004). DOI: 10.1214/aop/1079021462


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.


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Peter Becker-Kern. Mark M. Meerschaert. Hans-Peter Scheffler. "Limit theorems for coupled continuous time random walks." Ann. Probab. 32 (1B) 730 - 756, January 2004.


Published: January 2004
First available in Project Euclid: 11 March 2004

zbMATH: 1054.60052
MathSciNet: MR2039941
Digital Object Identifier: 10.1214/aop/1079021462

Primary: 60F17 , 60G50
Secondary: 60H30 , 82C31

Keywords: Continuous time random walk , fractional derivative , Functional limit theorem , operator stable law

Rights: Copyright © 2004 Institute of Mathematical Statistics


Vol.32 • No. 1B • January 2004
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