Random walk model for coordinate-dependent diffusion in a force field

In this paper we develop a random walk model on lattice for coordinate-dependent diffusion at constant temperature. We employ here waiting time of the walker to get coordinate dependence diffusion. Such modeling keeps local isotropy process intact which is consistent with nature thermal noise. The presence confining conservative force modeled by appropriately breaking jumps its nearest points. show that equilibrium characterized position distribution modified Boltzmann form as obtained an Itô process. also argue that, in such systems diffusivity, correctly captures transition over potential barrier opposed distribution. • Local Stokes–Einstein relation dependent Modified under Barrier overcoming