Monotonicity of escape probabilities for branching random walks on Zd

Achillefs Tzioufas

Statistics & Probability Letters, 2020, vol. 167, issue C

Abstract: We study nearest-neighbors branching random walks started from a point at the interior of a hypercube. We show that the probability that the process escapes the hypercube is monotonically decreasing with respect to the distance of its starting point from the boundary. We derive as a consequence that at all times the number of particles at a site is monotonically decreasing with respect to its distance from the starting point.

Keywords: Branching random walks; Spatial-symmetry stochastic comparisons (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1016/j.spl.2020.108900

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