{"paper":{"title":"Smearing Distributions and their use in Financial Markets","license":"","headline":"","cross_cats":["cond-mat.stat-mech","physics.soc-ph"],"primary_cat":"q-fin.ST","authors_text":"Hagen Kleinert, Petr Jizba","submitted_at":"2007-12-03T16:17:53Z","abstract_excerpt":"It is shown that superpositions of path integrals with arbitrary Hamiltonians and different scaling parameters v (\"variances\") obey the Chapman-Kolmogorov relation for Markovian processes if and only if the corresponding smearing distributions for v have a specific functional form. Ensuing \"smearing\" distributions substantially simplify the coupled system of Fokker-Planck equations for smeared and un-smeared conditional probabilities. Simple application in financial models with stochastic volatility is presented."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0712.0083","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"}