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Reflecting random walks in curvilinear wedges

Menshikov, Mikhail V.; Mijatović, Aleksandar; Wade, Andrew R.

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Authors

Aleksandar Mijatović



Contributors

M.E. Vares
Editor

R. Fernández
Editor

L.R. Fontes
Editor

C.M. Newman
Editor

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.

Citation

Menshikov, M. V., Mijatović, A., & Wade, A. R. (2021). Reflecting random walks in curvilinear wedges. In M. Vares, R. Fernández, L. Fontes, & C. Newman (Eds.), In and out of equilibrium 3: celebrating Vladas Sidoarvicius (637-675). Springer Verlag. https://doi.org/10.1007/978-3-030-60754-8_26

Acceptance Date Jun 22, 2020
Publication Date 2021
Deposit Date Jun 19, 2020
Publicly Available Date Mar 28, 2024
Publisher Springer Verlag
Pages 637-675
Series Title Progress in probability
Series Number 77
Book Title In and out of equilibrium 3: celebrating Vladas Sidoarvicius.
ISBN 9783030607531
DOI https://doi.org/10.1007/978-3-030-60754-8_26
Publisher URL https://www.springer.com/gp/book/9783030607531
Related Public URLs https://arxiv.org/abs/2001.06685

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