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Record statistics and persistence for a random walk with a drift


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  • Satya N. Majumdar
  • Gregory Schehr
  • Gregor Wergen
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    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 L\'evy index 0 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

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    Bibliographic Info

    Paper provided by in its series Papers with number 1206.6972.

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    Date of creation: Jun 2012
    Date of revision: Aug 2012
    Publication status: Published in J. Phys. A: Math. Theor. 45 (2012) 355002
    Handle: RePEc:arx:papers:1206.6972

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    Cited by:
    1. Gregory Schehr & Satya N. Majumdar, 2013. "Exact record and order statistics of random walks via first-passage ideas," Papers 1305.0639,
    2. Wergen, Gregor, 2014. "Modeling record-breaking stock prices," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 396(C), pages 114-133.


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