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

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.