{"id":"W4387362664","doi":"10.1080/27684520.2023.2261429","title":"A proof and an application of the continuous parameter martingale convergence theorem","year":2023,"lang":"en","type":"article","venue":"Research in Statistics","topic":"Stochastic processes and financial applications","field":"Economics, Econometrics and Finance","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Ottawa","funders":"","keywords":"Martingale (probability theory); Local martingale; Mathematics; Martingale difference sequence; Optional stopping theorem; Doob's martingale inequality; Dominated convergence theorem; Probabilistic logic; Weak convergence; Applied mathematics; Bounded function; Pure mathematics; Discrete mathematics; Convergence tests; Mathematical analysis; Rate of convergence; Computer science","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001128782,0.0000490483,0.0001381153,0.0001211544,0.00009436552,0.00002164621,0.0002059985,0.00004018794,0.000009163007],"category_scores_gemma":[0.0006722822,0.00004477078,0.000011726,0.0007876659,0.0002406025,0.00004470399,0.00009921744,0.0001437915,0.00004682792],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002297988,"about_ca_system_score_gemma":0.00002981875,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0002651526,"about_ca_topic_score_gemma":0.00006653399,"domain_scores_codex":[0.9991748,0.00001631449,0.0003052817,0.0002160774,0.00006856878,0.000218916],"domain_scores_gemma":[0.9991353,0.0003629167,0.0001129278,0.0002624292,0.00008652059,0.00003986634],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.000006489998,0.00003534397,0.02864489,0.00004767987,0.000002220462,5.053354e-7,0.0002686561,0.00001300185,0.00006011986,0.9634147,0.0001382209,0.00736816],"study_design_scores_gemma":[0.0001188804,0.00004450952,0.08098024,0.00001023155,7.767059e-7,6.084844e-7,0.000103325,0.0394784,0.00009868501,0.87774,0.00136957,0.00005475037],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.160794,0.0002649588,0.8352795,0.0005379827,0.00007737178,0.0008416453,0.000853875,0.00001961803,0.001331009],"genre_scores_gemma":[0.9963858,0.00005055207,0.00322451,0.0000154623,0.00002658868,0.0001913463,0.00001230764,0.000009180003,0.00008427],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.8355917,"threshold_uncertainty_score":0.1825699,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.09324678482625785,"score_gpt":0.3605287071007934,"score_spread":0.2672819222745356,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}