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On Seneta–Heyde scaling for a stable branching random walk
Published online by Cambridge University Press: 26 July 2018
Abstract
We consider a discrete-time branching random walk in the boundary case, where the associated random walk is in the domain of attraction of an α-stable law with 1 < α < 2. We prove that the derivative martingale Dn converges to a nontrivial limit D∞ under some regular conditions. We also study the additive martingale Wn and prove that n1/αWn converges in probability to a constant multiple of D∞.
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- Copyright © Applied Probability Trust 2018
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