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Stochastic Process with Ultraslow Convergence to a Gaussian: The Truncated Lévy Flight
Abstract
We introduce a class of stochastic process, the truncated L\'evy flight (TLF), in which the arbitrarily large steps of a L\'evy flight are eliminated. We find that the convergence of the sum of $n$ independent TLFs to a Gaussian process can require a remarkably large value of $n$---typically $n\ensuremath{\approx}{10}^{4}$ in contrast to $n\ensuremath{\approx}10$ for common distributions. We find a well-defined crossover between a L\'evy and a Gaussian regime, and that the crossover carries information about the relevant parameters of the underlying stochastic process.
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Cites
Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications
Bouchaud, J.-P., & Georges, A. (1990) · Physics Reports · doi:10.1016/0370-1573(90)90099-n · Cited by 4,162
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Limits of Predictability in Human Mobility
Song, C., Qu, Z., Blumm, N., & Barabási, A.-L. (2010) · Science · doi:10.1126/science.1177170 · Cited by 3,234
Optimizing the success of random searches.
Viswanathan, G. M., Buldyrev, S. V., Havlin, S., da Luz, M. G. E., Raposo, E. P., & Stanley, H. E. (1999) · Nature · doi:10.1038/44831 · Cited by 1,359
Self-citationVermeersch, B., Mohammed, A. M. S., Pernot, G., Koh, Y. R., & Shakouri, A. (2015) · Physical Review B · doi:10.1103/physrevb.91.085203 · Cited by 78
Metadata
- Authors
- Mantegna, R. N., & Stanley, H. E.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 1994-11-28
- Volume
- 73
- Issue
- 22
- Pages
- 2946-2949
- ISSN
- 0031-9007 (ISSN-L)
- OpenAlex
- W2048421273
- Cited by
- 880
- References
- 1
- FWCI
- 4.92
- Type
- journal article
- Language
- en
- Open access
- closed
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