{"paper":{"title":"State-dependent Fractional Point Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Enzo Orsingher, Federico Polito, Roberto Garra","submitted_at":"2013-03-26T23:01:53Z","abstract_excerpt":"The aim of this paper is the analysis of the fractional Poisson process where the state probabilities $p_k^{\\nu_k}(t)$, $t\\ge 0$, are governed by time-fractional equations of order $0<\\nu_k\\leq 1$ depending on the number $k$ of events occurred up to time $t$. We are able to obtain explicitely the Laplace transform of $p_k^{\\nu_k}(t)$ and various representations of state probabilities. We show that the Poisson process with intermediate waiting times depending on $\\nu_k$ differs from that constructed from the fractional state equations (in the case $\\nu_k = \\nu$, for all $k$, they coincide with "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.6699","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":""},"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"}