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First-passage properties of asymmetric Lévy flights


First-passage properties of asymmetric Lévy flights

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dc.contributor.author Padash, Amin pl
dc.contributor.author Chechkin, Aleksei V. pl
dc.contributor.author Dybiec, Bartłomiej [SAP11018789] pl
dc.contributor.author Pavlyukevich, Ilya pl
dc.contributor.author Shokri, Babak pl
dc.contributor.author Metzler, Ralf pl
dc.date.accessioned 2019-11-04T10:29:03Z
dc.date.available 2019-11-04T10:29:03Z
dc.date.issued 2019 pl
dc.identifier.issn 1751-8113 pl
dc.identifier.uri https://ruj.uj.edu.pl/xmlui/handle/item/86316
dc.language eng pl
dc.rights Udzielam licencji. Uznanie autorstwa 3.0 *
dc.rights.uri http://creativecommons.org/licenses/by/3.0/legalcode *
dc.title First-passage properties of asymmetric Lévy flights pl
dc.type JournalArticle pl
dc.abstract.en Lévy flights are paradigmatic generalised random walk processes, in which the independent stationary increments—the 'jump lengths'—are drawn from an -stable jump length distribution with long-tailed, power-law asymptote. As a result, the variance of Lévy flights diverges and the trajectory is characterised by occasional extremely long jumps. Such long jumps significantly decrease the probability to revisit previous points of visitation, rendering Lévy flights efficient search processes in one and two dimensions. To further quantify their precise property as random search strategies we here study the first-passage time properties of Lévy flights in one-dimensional semi-infinite and bounded domains for symmetric and asymmetric jump length distributions. To obtain the full probability density function of first-passage times for these cases we employ two complementary methods. One approach is based on the space-fractional diffusion equation for the probability density function, from which the survival probability is obtained for different values of the stable index and the skewness (asymmetry) parameter . The other approach is based on the stochastic Langevin equation with -stable driving noise. Both methods have their advantages and disadvantages for explicit calculations and numerical evaluation, and the complementary approach involving both methods will be profitable for concrete applications. We also make use of the Skorokhod theorem for processes with independent increments and demonstrate that the numerical results are in good agreement with the analytical expressions for the probability density function of the first-passage times. pl
dc.description.volume 52 pl
dc.description.number 45 pl
dc.identifier.doi 10.1088/1751-8121/ab493e pl
dc.identifier.eissn 1751-8121 pl
dc.title.journal Journal of Physics. A, Mathematical and Theoretical pl
dc.language.container eng pl
dc.affiliation Wydział Fizyki, Astronomii i Informatyki Stosowanej : Instytut Fizyki im. Mariana Smoluchowskiego pl
dc.subtype Article pl
dc.identifier.articleid 454004 pl
dc.rights.original CC-BY; inne; ostateczna wersja wydawcy; w momencie opublikowania; 0 pl
dc.identifier.project ROD UJ / OP pl
.pointsMNiSW [2019 A]: 70

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Udzielam licencji. Uznanie autorstwa 3.0 Except where otherwise noted, this item's license is described as Udzielam licencji. Uznanie autorstwa 3.0