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Description
Escape kinetics of a stochastic process can be influenced by imposing stochastic resetting, a protocol of starting anew. We study the escape kinetics from a finite interval restricted by two absorbing boundaries in the presence of heavy-tailed, Lévy type, $\alpha$-stable noise. We find that the width of the domain where resetting is beneficial depends on the value of the stability index $\alpha$ determining the jump length distribution. The domain is narrower for heavier (smaller $\alpha$) distributions in comparison to lighter tails. Additionally, we explore connections between Lévy flights (LF) and Lévy walks (LW) in presence of stochastic resetting. In the domain characterized by a finite mean jump duration/length, with increasing interval width, LF and LW start to share similarities. However, for small intervals, resetting can be beneficial for LW also in the domain where the coefficient of variation is smaller than 1, which wasn't observed in case of LF.
[1] B. Żbik, and B. Dybiec, Phys. Rev. E 109, 044147 (2024).
