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On $L^p$-convergence of the Biggins martingale with complex parameter
- Publication Year :
- 2019
-
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 $p\in (1,2)$) than those for the Biggins martingale with real parameter. Our conditions are ultimate in the case $p\geq 2$ only.<br />Comment: submitted, 16 pages
- Subjects :
- Mathematics - Probability
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1903.00524
- Document Type :
- Working Paper