{"id":"W1799482306","doi":"10.1090/fic/044/04","title":"Four limit theorems for quadratic functionals of Brownian motion and Brownian bridge","year":2004,"lang":"en","type":"preprint","venue":"","topic":"Stochastic processes and financial applications","field":"Economics, Econometrics and Finance","cited_by":27,"is_retracted":false,"has_abstract":true,"ca_institutions":"Carleton University","funders":"","keywords":"Brownian motion; Limit (mathematics); Brownian bridge; Brownian excursion; Quadratic equation; Quadratic variation; Mathematics; Bridge (graph theory); Statistical physics; Diffusion process; Mathematical analysis; Geometric Brownian motion; Mathematical physics; Physics; Classical mechanics; Geometry; Computer science; Statistics","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":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0003256793,0.0002351666,0.0005865598,0.0002186852,0.000109108,0.00006759125,0.0002254118,0.0002904547,0.00008546924],"category_scores_gemma":[0.0002035046,0.0002644909,0.0001895537,0.000142636,0.0001001423,0.0000827773,0.0001533372,0.0001831986,0.0000466157],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00008340873,"about_ca_system_score_gemma":0.00008010668,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0006158007,"about_ca_topic_score_gemma":0.00008447836,"domain_scores_codex":[0.99831,0.000002481907,0.0008074644,0.0006123009,0.00004246514,0.0002252889],"domain_scores_gemma":[0.9986418,0.0001014061,0.0006556008,0.0003967118,0.0001247144,0.00007970274],"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":[0.00001865647,0.00008691622,0.0006378942,0.0003927303,0.00005220177,1.33594e-7,0.0001347904,0.0003016235,0.000008214366,0.9949286,0.0000890089,0.00334921],"study_design_scores_gemma":[0.0004518742,0.00007559005,0.04407504,0.00006018084,0.00002556197,0.000003638867,0.00001855439,0.002773512,0.00003513566,0.9505643,0.001630814,0.0002857641],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.01010852,0.001367141,0.9790608,0.001231231,0.0003701775,0.0009504828,0.0009988627,0.0000430468,0.005869759],"genre_scores_gemma":[0.9899147,0.0001467075,0.008503307,0.000180017,0.0002574792,0.0004499089,0.0001370461,0.00003697961,0.0003738611],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.9798062,"threshold_uncertainty_score":0.9999807,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.07855772757865495,"score_gpt":0.244695226718433,"score_spread":0.1661374991397781,"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."}}