Continuous Time Random Walks And Lévy Walks With Stochastic Resetting

Basing on the theory of continuous time random walk(CTRW)and Lévy walk,we build up the theory of the corresponding processes with stochastic resetting regarding to a resetting rate r.The reset position is prescribed in this paper.Next the stationary probability density functions and mean squared displacements(MSDs)are also calculated to show the influences of stochastic resetting on the CTRW and Lévy walk model.From the results,the stochastic resetting always makes the CTRW process localization and the Lévy walk diffuses slower comparing with the zero resetting rate.And the asymptotic behavior of PDF of stochastic resetting Lévy walk is also calculated by considering different scales of x and t,which also indicates the influence of the stochastic resetting.