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FRACTAL DIMENSION RESULTS FOR CONTINUOUS TIME RANDOM WALKS
Mark M Meerschaert1, Erkan Nane, Yimin Xiao
1Department of Probability and Statistics, Michigan State University, East Lansing, MI 48824, mcubed@stt.msu.edu URL: http://www.stt.msu.edu/users/mcubed/
Statistics & Probability Letters
|March 14, 2013
Summary
Continuous time random walks introduce random waiting times for particle movement. This study calculates the fractal dimensions of these processes, characterizing particle traces in anomalous diffusion.
Area of Science:
- Physics
- Mathematics
- Physical Chemistry
Background:
- Anomalous diffusion describes particle transport deviating from Brownian motion.
- Continuous time random walks (CTRWs) model systems with non-exponential waiting time distributions between jumps.
Purpose of the Study:
- To compute the fractal dimensions of continuous time random walks (CTRWs) process limits.
- To characterize particle traces in anomalous diffusion using fractal geometry.
Main Methods:
- Mathematical analysis of CTRWs.
- Calculation of fractal dimensions for stochastic processes.
Main Results:
- The fractal dimensions of CTRW process limits were successfully computed.
- These dimensions provide a quantitative measure of particle trace complexity in anomalous diffusion.
Conclusions:
- The fractal dimension is a key parameter for understanding anomalous diffusion phenomena.
- CTRWs offer a robust framework for modeling and analyzing complex particle transport.
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