{"paper":{"title":"L\\'evy processes, martingales, reversed martingales and orthogonal polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Pawe{\\l} J. Szab{\\l}owski","submitted_at":"2012-12-13T10:51:44Z","abstract_excerpt":"We study class of L\\'{e}vy processes having distributions being indentifiable by moments. We define system of polynomial martingales \\newline $\\left\\{ M_{n}(X_{t},t),\\mathcal{F}_{\\leq t}\\right\\} _{n\\geq 1},$ where $% \\mathcal{F}_{\\leq t}$ is a suitable filtration defined below. We present several properties of these martingales. Among others we show that $% M_{1}(X_{t},t)/t$ is a reversed martingale as well as a harness. Main results of the paper concern the question if martingale say $M_{i}$ multiplied by suitable determinstic function $\\mu _{i}(t)$ is a reversed martingale. We show that for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.3121","kind":"arxiv","version":5},"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"}