A continuous-time random walk extension of the Gillis model

Abstract

We consider a continuous-time random walk which is the generalization, by means of the introduction of waiting periods on sites, of the one-dimensional nonhomogeneous random walk with a position-dependent drift known in the mathematical literature as Gillis random walk. This modified stochastic process allows to significantly change local, non-local and transport properties in the presence of heavy-tailed waiting-time distributions lacking the first moment: we provide here exact results concerning hitting times, first-time events, survival probabilities, occupation times, the moments spectrum and the statistics of records. Specifically, normal diffusion gives way to subdiffusion and we are witnessing the breaking of ergodicity. Furthermore we also test our theoretical predictions with numerical simulations.

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Cited by in corpus (7)

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• First-passage functionals of Brownian motion in logarithmic potentials and heterogeneous diffusion
• A sluggish random walk with subdiffusive spread
• Optimal conditions for first passage of jump processes with resetting
• Extreme value statistics of positive recurrent centrally biased random walks
• Non-homogeneous random walks with stochastic resetting: an application to the Gillis model