{"id":"W1965277094","doi":"10.1016/j.insmatheco.2007.03.001","title":"Stock exchange fractional dynamics defined as fractional exponential growth driven by (usual) Gaussian white noise. Application to fractional Black–Scholes equations","year":2007,"lang":"en","type":"article","venue":"Insurance Mathematics and Economics","topic":"Complex Systems and Time Series Analysis","field":"Economics, Econometrics and Finance","cited_by":113,"is_retracted":false,"has_abstract":false,"ca_institutions":"Université du Québec à Montréal","funders":"","keywords":"Fractional Brownian motion; Mathematics; Fractional calculus; Exponential function; Applied mathematics; White noise; Mathematical analysis; Brownian motion","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.00090627,0.0005947545,0.0005257307,0.0007692325,0.000288448,0.00130605,0.000414855,0.0009673145,0.001754924],"category_scores_gemma":[0.004311743,0.000201544,0.0006458723,0.000516152,0.001125011,0.001998218,0.0007764117,0.0008129893,0.0001111918],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0006741719,"about_ca_system_score_gemma":0.0004829699,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002335654,"about_ca_topic_score_gemma":0.001219044,"domain_scores_codex":[0.9998468,0.00004157774,0.00001127335,0.00003561121,0.00004071798,0.00002389089],"domain_scores_gemma":[0.9991947,0.0002968635,0.0002290438,0.00005482475,0.0001161593,0.0001084657],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.00006020981,0.00002616641,0.001665466,0.0000501647,0.00004435513,0.0003148361,0.0001500704,0.07677577,0.005475961,0.9058723,0.001143505,0.008421144],"study_design_scores_gemma":[0.00001873534,0.00002083733,0.001065057,0.00001392315,0.00002111439,0.0001694161,0.00004282954,0.776948,0.0007719714,0.219339,0.001566155,0.00002299134],"study_design_candidate":"simulation_or_modeling","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.4356981,0.002966984,0.5419699,0.002866261,0.0007100323,0.000028839,0.0002871477,0.0002248445,0.01524801],"genre_scores_gemma":[0.9814954,0.001238614,0.009710805,0.0001436342,0.0002350857,0.00002001499,0.00007647851,0.00002880554,0.00705109],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.002335654,"threshold_uncertainty_score":0.005870759,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01725178075045566,"score_gpt":0.2269684155407933,"score_spread":0.2097166347903377,"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."}}