Average Time Spent by a Levy Flyer on an Interval with Absorbing Boundaries

@inproceedings{Buldyrev2000AverageTS,
  title={Average Time Spent by a Levy Flyer on an Interval with Absorbing Boundaries},
  author={Sergey V. Buldyrev and Shlomo Havlin and Alexander Ya. Kazakov and Marcos G. E. da Luz and Ernesto P. Raposo and Harry Eugene Stanley and Gandhimohan M. Viswanathan},
  year={2000}
}
We consider a Lévy flyer that starts from a point x0 on an interval [O,L] with absorbing boundaries. Using fractional differential equations, we show that the average number of flights the flyer takes before it is absorbed is 2(πα)−1 sin(πα/2) [ x0(L − x0)l −2 0 ]α/2 , where 0 < α < 2 and l0 > 0 are the parameters of the distribution of the flight length l: P (|l| > r) = (l0/r) α, r > l0, and l0 is a small number with respect to x0 and L − x0. For α > 2, when the second moment of the flight… CONTINUE READING

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