Abstract
We consider a branching random walk. Biggins and Kyprianou (2004) proved that, in the boundary case, the associated derivative martingale converges almost surely to a finite nonnegative limit, whose law serves as a fixed point of a smoothing transformation (Mandelbrot's cascade). In this paper, we give a necessary and sufficient condition for the nontriviality of the limit in this boundary case.
Citation
Xinxin Chen. "A necessary and sufficient condition for the nontrivial limit of the derivative martingale in a branching random walk." Adv. in Appl. Probab. 47 (3) 741 - 760, September 2015. https://doi.org/10.1239/aap/1444308880
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