{"paper":{"title":"On Seneta-Heyde Scaling for a stable branching random walk","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Hui He, Jingning Liu, Mei Zhang","submitted_at":"2016-10-12T01:41:13Z","abstract_excerpt":"We consider a discrete-time branching random walk in the boundary case, where the associated random walk is in the domain of attraction of an $\\alpha$-stable law with $1<\\alpha<2$. We prove that the derivative martingale $D_n$ converges to a non-trivial limit $D_\\infty$ under some regular conditions. We also study the additive martingale $W_n$, and prove $n^\\frac{1}{\\alpha}W_n$ converges in probability to a constant multiple of $D_\\infty$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.03575","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}