First-passage-time exponent for higher-order random walks: Using Lévy flights

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Abstract

A relation between the shift in the first-passage-time exponent and the decay rate of the probability of N velocity zero crossings for the nth random walk is presented. By slicing time in terms of velocity zero crossings, higher-order random walks are characterized in terms of a one-dimensional Lévy process.

Original languageEnglish (US)
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume64
Issue number1 II
StatePublished - Jul 2001
Externally publishedYes

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Zero-crossing
roots of equations
First Passage Time
random walk
Random walk
Exponent
flight
exponents
Higher Order
slicing
Slicing
Decay Rate
decay rates
shift

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Condensed Matter Physics
  • Statistical and Nonlinear Physics

Cite this

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abstract = "A relation between the shift in the first-passage-time exponent and the decay rate of the probability of N velocity zero crossings for the nth random walk is presented. By slicing time in terms of velocity zero crossings, higher-order random walks are characterized in terms of a one-dimensional L{\'e}vy process.",
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AB - A relation between the shift in the first-passage-time exponent and the decay rate of the probability of N velocity zero crossings for the nth random walk is presented. By slicing time in terms of velocity zero crossings, higher-order random walks are characterized in terms of a one-dimensional Lévy process.

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