Abstract
What happens when a continuously evolving stochastic process is interrupted with large changes at random intervals distributed as a power law ? 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 , to one that is time independent for . 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 that minimizes the mean time to reach the target, thereby offering a step towards a viable strategy to locate targets in a crowded environment.
- Received 11 December 2015
- Revised 18 April 2016
DOI:https://doi.org/10.1103/PhysRevE.93.060102
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