On $L^p$-convergence of the Biggins martingale with complex parameter
| Autor: | Iksanov, Alexander, Liang, Xingang, Liu, Quansheng |
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| Rok vydání: | 2019 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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 $p\in (1,2)$) than those for the Biggins martingale with real parameter. Our conditions are ultimate in the case $p\geq 2$ only. Comment: submitted, 16 pages |
| Databáze: | arXiv |
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