{"paper":{"title":"Fractional counting process at L\\'evy times and its applications","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Aditya Maheshwari, Ashok Kumar Pathak, Shilpa Garg","submitted_at":"2024-12-05T16:49:02Z","abstract_excerpt":"Traditionally, fractional counting processes, such as the fractional Poisson process, etc. have been defined using fractional differential and integral operators. Recently, Laskin (2024) introduced a generalized fractional counting process (FCP) by changing the probability mass function (pmf) of the time fractional Poisson process using the generalized three-parameter Mittag-Leffler function. Here, we study some additional properties for the FCP and introduce a time-changed fractional counting process (TCFCP), defined by time-changing the FCP with an independent L\\'evy subordinator. We derive "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.04334","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.04334/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"}