|
Hokkaido University Collection of Scholarly and Academic Papers >
Graduate School of Information Science and Technology / Faculty of Information Science and Technology >
Peer-reviewed Journal Articles, etc >
Crossover between Lévy and Gaussian regimes in first-passage processes
| Title: | Crossover between Lévy and Gaussian regimes in first-passage processes |
| Authors: | Inoue, Jun-ichi Browse this author →KAKEN DB | | Sazuka, Naoya Browse this author |
| Issue Date: | 17-Aug-2007 |
| Publisher: | American Physical Society |
| Journal Title: | Physical Review E |
| Volume: | 76 |
| Issue: | 2 |
| Start Page: | 021111 |
| Publisher DOI: | 10.1103/PhysRevE.76.021111 |
| PMID: | 17930010 |
| Abstract: | We propose an approach to the problem of the first-passage time. Our method is applicable not only to the Wiener process but also to the non-Gaussian Lévy flights or to more complicated stochastic processes whose distributions are stable. To show the usefulness of the method, we particularly focus on the first-passage time problems in the truncated Lévy flights (the so-called KoBoL processes from Koponen, Boyarchenko, and Levendorskii), in which the arbitrarily large tail of the Lévy distribution is cut off. We find that the asymptotic scaling law of the first-passage time t distribution changes from t−(+1)/-law (non-Gaussian Lévy regime) to t−3/2-law (Gaussian regime) at the crossover point. This result means that an ultraslow convergence from the non-Gaussian Lévy regime to the Gaussian regime is observed not only in the distribution of the real time step for the truncated Lévy flight but also in the first-passage time distribution of the flight. The nature of the crossover in the scaling laws and the scaling relation on the crossover point with respect to the effective cutoff length of the Lévy distribution are discussed. |
| Rights: | Copyright © 2007 American Physical Society |
| Relation: | http://www.aps.org/ |
| Type: | article |
| URI: | http://hdl.handle.net/2115/28043 |
| Appears in Collections: | 情報科学院・情報科学研究院 (Graduate School of Information Science and Technology / Faculty of Information Science and Technology) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
|
Submitter: 井上 純一
|
