Majumdar, Satya N., Schehr, Gregory and Wergen, Gregor (2012). Record statistics and persistence for a random walk with a drift. J. Phys. A-Math. Theor., 45 (35). BRISTOL: IOP PUBLISHING LTD. ISSN 1751-8121
Full text not available from this repository.Abstract
We study the statistics of records of a one-dimensional random walk of n steps, starting from the origin, and in the presence of a constant bias c. At each time step, the walker makes a random jump of length. drawn from a continuous distribution f(eta), which is symmetric around a constant drift c. We focus in particular on the case where f (eta) is a symmetric stable law with a Levy index 0 < mu <= 2. The record statistics crucially depends on the persistence probability, which, as we show here, exhibits different behaviors depending on the sign of c and the value of the parameter mu. Hence, in the limit of a large number of steps n, the record statistics is sensitive to these parameters (c and mu) of the jump distribution. We compute the asymptotic mean record number < R-n > after n steps as well as its full distribution P (R, n). We also compute the statistics of the ages of the longest and the shortest lasting record. Our exact computations show the existence of five distinct regions in the (c, 0 < mu <= 2) strip where these quantities display qualitatively different behaviors. We also present numerical simulation results that verify our analytical predictions.
Item Type: | Journal Article | ||||||||||||||||
Creators: |
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URN: | urn:nbn:de:hbz:38-483166 | ||||||||||||||||
DOI: | 10.1088/1751-8113/45/35/355002 | ||||||||||||||||
Journal or Publication Title: | J. Phys. A-Math. Theor. | ||||||||||||||||
Volume: | 45 | ||||||||||||||||
Number: | 35 | ||||||||||||||||
Date: | 2012 | ||||||||||||||||
Publisher: | IOP PUBLISHING LTD | ||||||||||||||||
Place of Publication: | BRISTOL | ||||||||||||||||
ISSN: | 1751-8121 | ||||||||||||||||
Language: | English | ||||||||||||||||
Faculty: | Unspecified | ||||||||||||||||
Divisions: | Unspecified | ||||||||||||||||
Subjects: | no entry | ||||||||||||||||
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URI: | http://kups.ub.uni-koeln.de/id/eprint/48316 |
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