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Reflecting random walks in curvilinear wedges.

Menshikov, Mikhail V. and Mijatović, Aleksandar and Wade, Andrew R. 'Reflecting random walks in curvilinear wedges.', in In and out of equilibrium 3: celebrating Vladas Sidoarvicius. , pp. 637-675. Progress in probability., 77

Abstract

We study a random walk (Markov chain) in an unbounded planar domain bounded by two curves of the form x2=a+xβ+1 and x2=−a−xβ−1 , with x1 ≥ 0. In the interior of the domain, the random walk has zero drift and a given increment covariance matrix. From the vicinity of the upper and lower sections of the boundary, the walk drifts back into the interior at a given angle α+ or α− to the relevant inwards-pointing normal vector. Here we focus on the case where α+ and α− are equal but opposite, which includes the case of normal reflection. For 0 ≤ β+, β− < 1, we identify the phase transition between recurrence and transience, depending on the model parameters, and quantify recurrence via moments of passage times.

Item Type:Book chapter
Full text:(AM) Accepted Manuscript
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Status:Peer-reviewed
Publisher Web site:https://www.springer.com/gp/book/9783030607531
Publisher statement:This a post-peer-review, pre-copyedit version of a chapter published in In and out of equilibrium 3: celebrating Vladas Sidoarvicius. The final authenticated version is available online at: https://doi.org/10.1007/978-3-030-60754-8_26
Date accepted:22 June 2020
Date deposited:08 December 2020
Date of first online publication:2021
Date first made open access:02 July 2022

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