The DOI matches its Crossref record; 6 of the 6 references it cites were found in a registry or an index.
Analytic approach to the problem of convergence of truncated Lévy flights towards the Gaussian stochastic process
Abstract
An analytic expression for characteristic function defining a truncated L\'evy flight is derived. It is shown that the characteristic function yields results in agreement with recent simulations of truncated L\'evy flights by Mantegna and Stanley [Phys. Rev. Lett. 73, 2946 (1994)]. With the analytic expression for the characteristic function, the convergence of the L\'evy process towards the Gaussian is demonstrated without simulations. In the calculation of first return probability the simulations are replaced by numerical integration using simple quadratures.
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Cites
The Fractal Geometry of Nature.
Sparrow, C., & Mandelbrot, B. (1984) · Journal of the Royal Statistical Society. Series A (General) · doi:10.2307/2981858 · Cited by 14,546
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
Limit Distributions for Sums of Independent Random Variables.
Lindley, D. V., Gnedenko, B. V., Kolmogorov, A. N., & Chung, K. L. (1955) · Journal of the Royal Statistical Society. Series A (General) · doi:10.2307/2343136 · Cited by 1,394
Shlesinger, M. F., Zaslavsky, G. M., & Klafter, J. (1993) · Nature · doi:10.1038/363031a0 · Cited by 1,051
Stochastic Process with Ultraslow Convergence to a Gaussian: The Truncated Lévy Flight
Mantegna, R. N., & Stanley, H. E. (1994) · Physical Review Letters · doi:10.1103/physrevlett.73.2946 · Cited by 880
Transport aspects in anomalous diffusion: Lévy walks
Blumen, A., Zumofen, G., & Klafter, J. (1989) · Physical Review A · doi:10.1103/physreva.40.3964 · Cited by 136
Cited by
Scaling of the distribution of fluctuations of financial market indices
Gopikrishnan, P., Plerou, V., Nunes Amaral, L. A., Meyer, M., & Stanley, H. E. (1999) · Physical Review E · doi:10.1103/physreve.60.5305 · Cited by 892
Physical approach to complex systems
Kwapień, J., & Drożdż, S. (2012) · Physics Reports · doi:10.1016/j.physrep.2012.01.007 · Cited by 517
Multifractal analysis of financial markets: a review
Jiang, Z.-Q., Xie, W.-J., Zhou, W.-X., & Sornette, D. (2019) · Reports on Progress in Physics · doi:10.1088/1361-6633/ab42fb · Cited by 423
Fluctuations of Lévy Processes with Applications: Introductory Lectures
Kyprianou, A. E. (2014) · Universitext · doi:10.1007/978-3-642-37632-0 · Cited by 373
Brantingham, P. J. (2006) · Current Anthropology · doi:10.1086/503062 · Cited by 111
Metadata
- Authors
- Koponen, I.
- Venue
- Physical Review E
- Publisher
- American Physical Society (APS)
- Published
- 1995-07-01
- Volume
- 52
- Issue
- 1
- Pages
- 1197-1199
- ISSN
- 1063-651X (ISSN-L)
- 1095-3787
- OpenAlex
- W1975760144
- Cited by
- 622
- References
- 6
- FWCI
- 1.47
- Type
- journal article
- Language
- en
- Open access
- closed
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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