Record statistics and persistence for a random walk with a drift

Satya N. Majumdar, Gregory Schehr and Gregor Wergen
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Satya N. Majumdar: LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques - UP11 - Université Paris-Sud - Paris 11 - CNRS - Centre National de la Recherche Scientifique
Gregory Schehr: LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques - UP11 - Université Paris-Sud - Paris 11 - CNRS - Centre National de la Recherche Scientifique
Gregor Wergen: Institut für Theoretische Physik [Köln] - Universität zu Köln = University of Cologne

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Abstract: We study the statistics of records of a one-dimensional random walk of n steps, starting from the origin, and in presence of a constant bias c. At each time-step the walker makes a random jump of length \eta drawn from a continuous distribution f(\eta) which is symmetric around a constant drift c. We focus in particular on the case were f(\eta) is a symmetric stable law with a Lévy index 0

Date: 2012
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Citations: View citations in EconPapers (6)

Published in Journal of Physics A General Physics (1968-1972), 2012, 45, pp.355002. ⟨10.1088/1751-8113/45/35/355002⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00744525

DOI: 10.1088/1751-8113/45/35/355002

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