Random walk with heterogeneous sojourn time
Analysis of PDEs
2023-02-14 v1 Probability
Abstract
We introduce a discrete-time random walk model on a one-dimensional lattice with a nonconstant sojourn time and prove that the discrete density converges to a solution of a continuum diffusion equation. Our random walk model is not Markovian due to the heterogeneity in the sojourn time, in contrast to a random walk model with a nonconstant walk length. We derive a Markovian process by choosing appropriate subindexes of the time-space grid points, and then show the convergence of its discrete density through the parabolic-scale limit. We also find the Green's function of the continuum diffusion equation and present three Monte Carlo simulations to validate the random walk model and the diffusion equation.
Cite
@article{arxiv.2302.06275,
title = {Random walk with heterogeneous sojourn time},
author = {Jaywan Chung and Yong-Jung Kim and Min-Gi Lee},
journal= {arXiv preprint arXiv:2302.06275},
year = {2023}
}