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Search reliability and search efficiency of combined Lévy-Brownian motion: Long relocations mingled with thorough local exploration

Research output: Contribution to journalArticleScientificpeer-review


Original languageEnglish
Article number394002
JournalJournal of Physics A: Mathematical and Theoretical
Issue number39
Publication statusPublished - 8 Sep 2016
Publication typeA1 Journal article-refereed


A combined dynamics consisting of Brownian motion and Lévy flights is exhibited by a variety of biological systems performing search processes. Assessing the search reliability of ever locating the target and the search efficiency of doing so economically of such dynamics thus poses an important problem. Here we model this dynamics by a one-dimensional fractional Fokker-Planck equation combining unbiased Brownian motion and Lévy flights. By solving this equation both analytically and numerically we show that the superposition of recurrent Brownian motion and Lévy flights with stable exponent α <1, by itself implying zero probability of hitting a point on a line, leads to transient motion with finite probability of hitting any point on the line. We present results for the exact dependence of the values of both the search reliability and the search efficiency on the distance between the starting and target positions as well as the choice of the scaling exponent α of the Lévy flight component.


  • Brownian motion, first arrival, first passage, Lévy flights, random search process

Publication forum classification

Field of science, Statistics Finland