{"paper":{"title":"Exponential Tail Estimates for Multitype Poisson Branching Processes and Application to Hawkes Processes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Th\\'eo Leblanc","submitted_at":"2025-07-11T10:06:58Z","abstract_excerpt":"We establish exponential moment bounds for linear functionals of the total progeny of multitype Poisson Bienaym\\'e-Galton-Watson trees. Our estimates are explicitly characterized in terms of the offspring mean matrix and the coefficients of the linear functional. As an application, we derive type-specific exponential moment bounds for multitype Hawkes processes, yielding improved results in high-dimensional settings. We also obtain exponential tail estimates for inhomogeneous Poisson clusters, with bounds that reflect the decay properties of the interaction kernels defining the clusters. These"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.08462","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.08462/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}