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  First passage and first hitting times of Levy flights and Levy walks

Palyulin, V. V., Blackburn, G., Lomholt, M. A., Watkins, N. W., Metzler, R., Klages, R., et al. (2019). First passage and first hitting times of Levy flights and Levy walks. New Journal of Physics, 21(10): 103028. doi:10.1088/1367-2630/ab41bb.

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 Creators:
Palyulin, Vladimir V.1, Author
Blackburn, George2, Author           
Lomholt, Michael A.1, Author
Watkins, Nicholas W.1, Author
Metzler, Ralf1, Author
Klages, Rainer2, Author           
Chechkin, Aleksei V.1, Author
Affiliations:
1external, ou_persistent22              
2Max Planck Institute for the Physics of Complex Systems, Max Planck Society, ou_2117288              

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 MPIPKS: Stochastic processes
 Abstract: For both Levy flight and Levy walk search processes we analyse the full distribution of first-passage and first-hitting (or first-arrival) times. These are, respectively, the times when the particle moves across a point at some given distance from its initial position for the first time, or when it lands at a given point for the first time. For Levy motions with their propensity for long relocation events and thus the possibility to jump across a given point in space without actually hitting it ('leapovers'), these two definitions lead to significantly different results. We study the first-passage and first-hitting time distributions as functions of the Levy stable index, highlighting the different behaviour for the cases when the first absolute moment of the jump length distribution is finite or infinite. In particular we examine the limits of short and long times. Our results will find their application in the mathematical modelling of random search processes as well as computer algorithms.

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 Dates: 2019-10-112019-10-01
 Publication Status: Issued
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 Identifiers: ISI: 000503455400028
DOI: 10.1088/1367-2630/ab41bb
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Title: New Journal of Physics
  Abbreviation : New J. Phys.
Source Genre: Journal
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Publ. Info: Bristol : IOP Publishing
Pages: - Volume / Issue: 21 (10) Sequence Number: 103028 Start / End Page: - Identifier: ISSN: 1367-2630
CoNE: https://pure.mpg.de/cone/journals/resource/954926913666