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First passage under restart has recently emerged as a conceptual framework tostudy various stochastic processes under restart mechanism. Emanating from thecanonical diffusion problem by Evans and Majumdar, restart has been shown tooutperform the completion of many first passage processes which otherwise wouldtake longer time to finish. However, most of the studies so far assumedcontinuous time underlying first passage time processes and moreover consideredcontinuous time resetting restricting out restart processes broken up intosynchronized time steps. To bridge this gap, in this paper, we study discretespace and time first passage processes under discrete time resetting in ageneral set-up. We sketch out the steps to compute the moments and theprobability density function which is often intractable in the continuous timerestarted process. A criterion that dictates when restart remains beneficial isthen derived. We apply our results to a symmetric and a biased random walker(RW) in one dimensional lattice confined within two absorbing boundaries.Numerical simulations are found to be in excellent agreement with thetheoretical results. Our method can be useful to understand the effect ofrestart on the spatiotemporal dynamics of confined lattice random walks inarbitrary dimensions.

First passage under restart for discrete space and time: application to one dimensional confined lattice random walks