On L^p-convergence of the Biggins martingale with complex parameter

2019/03/01 by Alexander Iksanov, Iksanov, Alexander, Xingang Liang +3
Mathematics · #FOS: Mathematics #Geometry and complex manifolds #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1903.00524

openalex publication_date 2019/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove necessary and sufficient conditions for the L^p-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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