{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ONF3XMUZ4JYUEKEPTJM7ICHWEO","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"923b3c3a39725e9a1e7ae0ce8137e55a0997d6e7d9aeeeae7e2f550d91102b65","cross_cats_sorted":["math.PR","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-06-04T07:00:46Z","title_canon_sha256":"6207de1813e82f20eb7577eae8e3c6c6668c05a165c9912c530c0cab8fbf918a"},"schema_version":"1.0","source":{"id":"1506.01478","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.01478","created_at":"2026-05-18T01:57:41Z"},{"alias_kind":"arxiv_version","alias_value":"1506.01478v1","created_at":"2026-05-18T01:57:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.01478","created_at":"2026-05-18T01:57:41Z"},{"alias_kind":"pith_short_12","alias_value":"ONF3XMUZ4JYU","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"ONF3XMUZ4JYUEKEP","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"ONF3XMUZ","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:e17551dfd9b58ca11196cde878d9666eed40b37a076cf0249df20fdeba89a6c8","target":"graph","created_at":"2026-05-18T01:57:41Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We construct a family of self-similar Markov martingales with given marginal distributions. This construction uses the self-similarity and Markov property of a reference process to produce a family of Markov processes that possess the same marginal distributions as the original process. The resulting processes are also self-similar with the same exponent as the original process. They can be chosen to be martingales under certain conditions. In this paper, we present two approaches to this construction, the transition-randomising approach and the time-change approach. We then compute the infini","authors_text":"Fima Klebaner, Jie Yen Fan, kais Hamza","cross_cats":["math.PR","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-06-04T07:00:46Z","title":"Mimicking self-similar processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.01478","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:6c00965be347be19d33f99bcb760f64ec267a3e0a03e2d38bf8e4c9510a01ba0","target":"record","created_at":"2026-05-18T01:57:41Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"923b3c3a39725e9a1e7ae0ce8137e55a0997d6e7d9aeeeae7e2f550d91102b65","cross_cats_sorted":["math.PR","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-06-04T07:00:46Z","title_canon_sha256":"6207de1813e82f20eb7577eae8e3c6c6668c05a165c9912c530c0cab8fbf918a"},"schema_version":"1.0","source":{"id":"1506.01478","kind":"arxiv","version":1}},"canonical_sha256":"734bbbb299e27142288f9a59f408f623a8e1482c2ae5fadf012e3fd90cd921bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"734bbbb299e27142288f9a59f408f623a8e1482c2ae5fadf012e3fd90cd921bc","first_computed_at":"2026-05-18T01:57:41.315916Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:57:41.315916Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e53/cpR0O8EFxhi/+ymZKa4uACGRZSp7zPWE/6jI3/zp4q1rgFEwUAA4JgL2JeDRevUrGh+pj4Mgo8aa1QM0Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:57:41.316629Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.01478","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6c00965be347be19d33f99bcb760f64ec267a3e0a03e2d38bf8e4c9510a01ba0","sha256:e17551dfd9b58ca11196cde878d9666eed40b37a076cf0249df20fdeba89a6c8"],"state_sha256":"644b9891306428c47132c34249bc98a899c9bf366eb2572193e48873de5442f6"}