{"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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.01187298,0.001601184,0.001379468,0.005267969,0.001801736,0.005491626,0.004744569,0.003329046,0.01035683],"category_scores_gemma":[0.02907842,0.0009024802,0.003692813,0.002557924,0.004396782,0.01144479,0.004489341,0.004428369,0.001729031],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002875872,"about_ca_system_score_gemma":0.00164984,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001126522,"about_ca_topic_score_gemma":0.0007983848,"domain_scores_codex":[0.9969702,0.0009272611,0.0002358675,0.0004843546,0.0009565852,0.0004255997],"domain_scores_gemma":[0.9855787,0.008550964,0.0008007238,0.001434819,0.002671687,0.000963103],"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":[0.00001939393,0.00002656343,0.0003077727,0.00006204081,0.0000208055,0.00007612396,0.0001542633,0.001577902,0.0004102581,0.9873842,0.001484129,0.008476504],"study_design_scores_gemma":[0.00001569321,0.00001908357,0.0003512595,0.00003864252,0.00002662267,0.000215876,0.00005244463,0.03167417,0.0007519686,0.962984,0.003844975,0.00002511866],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.04906561,0.003940113,0.8818458,0.003516643,0.0006659107,0.0001405785,0.0002220527,0.0003512525,0.06025219],"genre_scores_gemma":[0.6148719,0.005801426,0.2742878,0.002264922,0.001857588,0.0007480549,0.0007033258,0.0008534642,0.09861152],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01187298,"threshold_uncertainty_score":0.06279105,"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."}}