Asymptotic solutions of decoupled continuous-time random walks with superheavy-tailed waiting time and heavy-tailed jump length distributions
We study the long-time behavior of decoupled continuous-time random walks characterized by superheavy-tailed distributions of waiting times and symmetric heavy-tailed distributions of jump lengths. Our main quantity of interest is the limiting probability density of the position of the walker multip...
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| Veröffentlicht in: | Physical review. E, Statistical, nonlinear, and soft matter physics Statistical, nonlinear, and soft matter physics, 2011-12, Vol.84 (6 Pt 1), p.061143-061143, Article 061143 |
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| container_end_page | 061143 |
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| container_issue | 6 Pt 1 |
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| container_title | Physical review. E, Statistical, nonlinear, and soft matter physics |
| container_volume | 84 |
| creator | Denisov, S I Yuste, S B Bystrik, Yu S Kantz, H Lindenberg, K |
| description | We study the long-time behavior of decoupled continuous-time random walks characterized by superheavy-tailed distributions of waiting times and symmetric heavy-tailed distributions of jump lengths. Our main quantity of interest is the limiting probability density of the position of the walker multiplied by a scaling function of time. We show that the probability density of the scaled walker position converges in the long-time limit to a nondegenerate one only if the scaling function behaves in a certain way. This function as well as the limiting probability density are determined in explicit form. Also, we express the limiting probability density which has heavy tails in terms of the Fox H function and find its behavior for small and large distances. |
| doi_str_mv | 10.1103/PhysRevE.84.061143 |
| format | Article |
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| source | MEDLINE; American Physical Society Journals |
| subjects | Models, Theoretical Probability Stochastic Processes Time Factors |
| title | Asymptotic solutions of decoupled continuous-time random walks with superheavy-tailed waiting time and heavy-tailed jump length distributions |
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