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In this note we characterize under what conditions the limiting distribution of the ratios $V_{t}^{(k)} / m_{t}^{(k+1)}$ and $m_{t}^{(k+1)} / m_{t}^{(k)}$ exist, as $t \\downarrow0$ or $t \\to\\infty$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1407.3142","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-07-11T13:07:40Z","cross_cats_sorted":[],"title_canon_sha256":"6a3f24c7da90e1c0353b817c982b52af4b8cdf222936f14d15549898969ad698","abstract_canon_sha256":"0781911bea3f8fec3be367d9ddb840d77ba6a4c114dd5ffe5fbb7086d5ddbed7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:51.923602Z","signature_b64":"Ng+tsp9BfUjFo5ytY0jYAGh0E9JAnv7DSxA0Nm/F+qxQrbSLBNsIIsNCCxEqAcwzA+oCVWIBmoz+hABPqs2oDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b7f8f6bb4bdc2d25a9c1c17929eaf580c0190ca46378469dca90cb50c3c35ec","last_reissued_at":"2026-05-18T02:47:51.922919Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:51.922919Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The limit distribution of ratios of jumps and sums of jumps of subordinators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"David M. 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