Large deviation principle for the maximal positions in critical branching random walks with small drifts

Hongyan Sun and Lin Zhang

Statistics & Probability Letters, 2018, vol. 139, issue C, 31-39

Abstract: We consider critical branching random walks V(n),n≥1 on Z+. For fixed n, the displacement of an offspring from its parent is given by a nearest random walk with drift 2β∕nα towards the origin and reflected at the origin. For any κ>2α, let M[nκ](n) denote the rightmost position of the particles in [nκ]-th generation. We prove that, conditioned on survival to generation [nκ], M[nκ](n) satisfies a large deviation principle.

Keywords: Branching random walks; Large deviation principle; Galton–Watson process (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1016/j.spl.2018.03.011

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