Conditioned Two-Dimensional Simple Random Walk: Green’s Function and Harmonic Measure

Serguei Popov ()
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Serguei Popov: University of Campinas – UNICAMP

Journal of Theoretical Probability, 2021, vol. 34, issue 1, 418-437

Abstract: Abstract We study the Doob’s h-transform of the two-dimensional simple random walk with respect to its potential kernel, which can be thought of as the two-dimensional simple random walk conditioned on never hitting the origin. We derive an explicit formula for the Green’s function of this random walk and also prove a quantitative result on the speed of convergence of the (conditional) entrance measure to the harmonic measure (for the conditioned walk) on a finite set.

Keywords: Transience; Doob’s h-transform; Entrance measure; Primary 60J10; Secondary 60G50; 82C41 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10959-019-00963-4

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