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arXiv · 1909.07213

Continuous time random walks and L\'{e}vy walks with stochastic resetting

Tian Zhou·Pengbo Xu·Weihua Deng
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Abstract

Intermittent stochastic processes appear in a wide field, such as chemistry, biology, ecology, and computer science. This paper builds up the theory of intermittent continuous time random walk (CTRW) and L\'{e}vy walk, in which the particles are stochastically reset to a given position with a resetting rate $r$. The mean squared displacements of the CTRW and L\'{e}vy walks with stochastic resetting are calculated, uncovering that the stochastic resetting always makes the CTRW process localized and L\'{e}vy walk diffuse slower. The asymptotic behaviors of the probability density function of L\'evy walk with stochastic resetting are carefully analyzed under different scales of $x$, and a striking influence of stochastic resetting is observed.

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Tian Zhou, Pengbo Xu, Weihua Deng. 2019-09-13. Continuous time random walks and L\'{e}vy walks with stochastic resetting. https://doi.org/10.1103/physrevresearch.2.013103

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