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- W4320854555 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." @default.
- W4320854555 created "2023-02-16" @default.
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- W4320854555 date "2023-02-13" @default.
- W4320854555 modified "2023-09-28" @default.
- W4320854555 title "Random walk with heterogeneous sojourn time" @default.
- W4320854555 doi "https://doi.org/10.48550/arxiv.2302.06275" @default.
- W4320854555 hasPublicationYear "2023" @default.
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