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Reflecting random walks in curvilinear wedges
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Menshikov, Mikhail V., Mijatović, Aleksandar and Wade, Andrew R. (2020) Reflecting random walks in curvilinear wedges. In: Vares, M. E. and Fernández , R. and Fontes , L. R. and Newman , C. M. , (eds.) In and Out of Equilibrium 3 : Celebrating Vladas Sidoravicius. Progress in Probability, 77 . Cham: Birkhäuser, pp. 637-675. ISBN 9783030607531
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Official URL: http://dx.doi.org/10.1007/978-3-030-60754-8_26
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 Item | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||
Series Name: | Progress in Probability | ||||
Publisher: | Birkhäuser | ||||
Place of Publication: | Cham | ||||
ISBN: | 9783030607531 | ||||
ISSN: | 1050-6977 | ||||
Book Title: | In and Out of Equilibrium 3 : Celebrating Vladas Sidoravicius | ||||
Editor: | Vares, M. E. and Fernández , R. and Fontes , L. R. and Newman , C. M. | ||||
Official Date: | 4 November 2020 | ||||
Dates: |
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Volume: | 77 | ||||
Page Range: | pp. 637-675 | ||||
DOI: | 10.1007/978-3-030-60754-8_26 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published |
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