On L-convergence of the Biggins martingale with complex parameter
Résumé
We prove necessary and sufficient conditions for the Lp-convergence, p >1, of the Biggins martingale with complex parameter in the supercritical branching random walk. The results and their proofs are much more involved (especially in the case p ∈(1, 2)) than those for the Biggins martingale with real parameter. Our conditions are ultimate in the case p ≥2 only.
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