Diffusion with stochastic resetting at power-law times
What happens when a continuously evolving stochastic process is interrupted with large changes at random intervals τ distributed as a power law ∼τ^{-(1+α)};α>0? Modeling the stochastic process by diffusion and the large changes as abrupt resets to the initial condition, we obtain exact closed-for...
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| Published in | Physical review. E Vol. 93; no. 6; p. 060102 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
United States
01.06.2016
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| Online Access | Get more information |
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| Summary: | What happens when a continuously evolving stochastic process is interrupted with large changes at random intervals τ distributed as a power law ∼τ^{-(1+α)};α>0? Modeling the stochastic process by diffusion and the large changes as abrupt resets to the initial condition, we obtain exact closed-form expressions for both static and dynamic quantities, while accounting for strong correlations implied by a power law. Our results show that the resulting dynamics exhibits a spectrum of rich long-time behavior, from an ever-spreading spatial distribution for α<1, to one that is time independent for α>1. The dynamics has strong consequences on the time to reach a distant target for the first time; we specifically show that there exists an optimal α that minimizes the mean time to reach the target, thereby offering a step towards a viable strategy to locate targets in a crowded environment. |
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| ISSN: | 2470-0053 |
| DOI: | 10.1103/PhysRevE.93.060102 |