{"id":"W2962843786","doi":"10.1142/s0219493712500037","title":"FUKUSHIMA'S DECOMPOSITION FOR DIFFUSIONS ASSOCIATED WITH SEMI-DIRICHLET FORMS","year":2012,"lang":"en","type":"article","venue":"Stochastics and Dynamics","topic":"Advanced Mathematical Modeling in Engineering","field":"Computer Science","cited_by":7,"is_retracted":false,"has_abstract":true,"ca_institutions":"Concordia University","funders":"National Natural Science Foundation of China; Northwestern University","keywords":"Mathematics; Decomposition; Martingale (probability theory); Dirichlet distribution; Transformation (genetics); Local martingale; Diffusion; Applied mathematics; Pure mathematics; Mathematical analysis; Thermodynamics","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":[0.001588227,0.0009877811,0.0009646041,0.001912617,0.0007848671,0.002204875,0.0008128723,0.001185392,0.005460043],"category_scores_gemma":[0.004805094,0.0003245175,0.001247512,0.001150285,0.001968887,0.003100058,0.001222737,0.002230255,0.0008286613],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00106275,"about_ca_system_score_gemma":0.0005545795,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0007528106,"about_ca_topic_score_gemma":0.0004907561,"domain_scores_codex":[0.9993443,0.0001546367,0.00003803203,0.0001269272,0.0002210162,0.0001151602],"domain_scores_gemma":[0.9986011,0.0006032716,0.0002233251,0.0001080235,0.0003007317,0.0001635663],"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":[0.00002084877,0.0000162857,0.0002134316,0.00005801071,0.00001382876,0.00009720286,0.0001514571,0.004859253,0.002252728,0.98435,0.0005015738,0.007465453],"study_design_scores_gemma":[0.00001040937,0.00002604809,0.0005195304,0.000027358,0.00001264375,0.0002905704,0.00009617094,0.05314572,0.000923219,0.9420244,0.002903171,0.00002079329],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1136784,0.00263253,0.8497614,0.0009174998,0.0003296233,0.00006454244,0.0001722041,0.000102354,0.03234144],"genre_scores_gemma":[0.8779626,0.003223667,0.07941365,0.000317894,0.000543338,0.0001465109,0.0002860644,0.0001404007,0.03796585],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.005460043,"threshold_uncertainty_score":0.01826572,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.009567245296913064,"score_gpt":0.2501325814847704,"score_spread":0.2405653361878574,"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."}}