{"paper":{"title":"Some Time-changed fractional Poisson processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"A. Maheshwari, P. Vellaisamy","submitted_at":"2017-03-10T05:09:50Z","abstract_excerpt":"In this paper, we study the fractional Poisson process (FPP) time-changed by an independent L\\'evy subordinator and the inverse of the L\\'evy subordinator, which we call TCFPP-I and TCFPP-II, respectively. Various distributional properties of these processes are established. We show that, under certain conditions, the TCFPP-I has the long-range dependence property and also its law of iterated logarithm is proved. It is shown that the TCFPP-II is a renewal process and its waiting time distribution is identified. Its bivariate distributions and also the governing difference-differential equation"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.03547","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"}