{"paper":{"title":"Fractional Poisson processes and their representation by infinite systems of ordinary differential equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","stat.ME"],"primary_cat":"math.CA","authors_text":"Anthony W. Thomas, Ayse Kizilersu, Markus Kreer","submitted_at":"2013-10-11T15:16:42Z","abstract_excerpt":"Fractional Poisson processes, a rapidly growing area of non-Markovian stochastic processes, are useful in statistics to describe data from counting processes when waiting times are not exponentially distributed. We show that the fractional Kolmogorov-Feller equations for the probabilities at time t can be representated by an infinite linear system of ordinary differential equations of first order in a transformed time variable. These new equations resemble a linear version of the discrete coagulation-fragmentation equations, well-known from the non-equilibrium theory of gelation, cluster-dynam"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.3161","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"}