Rate of escape of the conditioned two-dimensional simple random walk

Orphée Collin and Serguei Popov

Stochastic Processes and their Applications, 2025, vol. 179, issue C

Abstract: We prove sharp asymptotic estimates for the rate of escape of the two-dimensional simple random walk conditioned to avoid a fixed finite set. We derive it from asymptotics available for the continuous analogue of this process (Collin and Comets, 2022), with the help of a KMT-type coupling adapted to this setup.

Keywords: Brownian motion; Conditioning; KMT approximation; Transience; Doob’s h-transform (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spa.2024.104469

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