{"id":"https://openalex.org/W4405757841","doi":"https://doi.org/10.3390/e27010002","title":"A Martingale-Free Introduction to Conditional Gaussian Nonlinear Systems","display_name":"A Martingale-Free Introduction to Conditional Gaussian Nonlinear Systems","publication_year":2024,"publication_date":"2024-12-24","ids":{"openalex":"https://openalex.org/W4405757841","doi":"https://doi.org/10.3390/e27010002","pmid":"https://pubmed.ncbi.nlm.nih.gov/39851622"},"language":"en","primary_location":{"id":"doi:10.3390/e27010002","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e27010002","pdf_url":"https://www.mdpi.com/1099-4300/27/1/2/pdf?version=1735051483","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/27/1/2/pdf?version=1735051483","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5106345140","display_name":"Marios Andreou","orcid":"https://orcid.org/0000-0002-7582-1386"},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Marios Andreou","raw_affiliation_strings":["Department of Mathematics, University of Wisconsin\u2013Madison, Madison, WI 53706, USA"],"raw_orcid":"https://orcid.org/0000-0002-7582-1386","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Wisconsin\u2013Madison, Madison, WI 53706, USA","institution_ids":["https://openalex.org/I135310074"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002818639","display_name":"Nan Chen","orcid":"https://orcid.org/0000-0002-9961-8905"},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Nan Chen","raw_affiliation_strings":["Department of Mathematics, University of Wisconsin\u2013Madison, Madison, WI 53706, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Wisconsin\u2013Madison, Madison, WI 53706, USA","institution_ids":["https://openalex.org/I135310074"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5106345140"],"corresponding_institution_ids":["https://openalex.org/I135310074"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.13378439,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"27","issue":"1","first_page":"2","last_page":"2"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10029","display_name":"Climate variability and models","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2306","display_name":"Global and Planetary Change"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10029","display_name":"Climate variability and models","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2306","display_name":"Global and Planetary Change"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10466","display_name":"Meteorological Phenomena and Simulations","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/1902","display_name":"Atmospheric Science"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10266","display_name":"Plant Water Relations and Carbon Dynamics","score":0.9929999709129333,"subfield":{"id":"https://openalex.org/subfields/2306","display_name":"Global and Planetary Change"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6403101682662964},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.6072463393211365},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6068277359008789},{"id":"https://openalex.org/keywords/intermittency","display_name":"Intermittency","score":0.5971053242683411},{"id":"https://openalex.org/keywords/conditional-expectation","display_name":"Conditional expectation","score":0.5311668515205383},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5252587199211121},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.523269534111023},{"id":"https://openalex.org/keywords/martingale","display_name":"Martingale (probability theory)","score":0.4666801691055298},{"id":"https://openalex.org/keywords/conditional-probability-distribution","display_name":"Conditional probability distribution","score":0.45561134815216064},{"id":"https://openalex.org/keywords/gaussian-process","display_name":"Gaussian process","score":0.4231802821159363},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4042391777038574},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.33075106143951416},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.1777724027633667},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17133629322052002},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0860343873500824}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6403101682662964},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.6072463393211365},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6068277359008789},{"id":"https://openalex.org/C2780388094","wikidata":"https://www.wikidata.org/wiki/Q1666248","display_name":"Intermittency","level":3,"score":0.5971053242683411},{"id":"https://openalex.org/C186215838","wikidata":"https://www.wikidata.org/wiki/Q772232","display_name":"Conditional expectation","level":2,"score":0.5311668515205383},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5252587199211121},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.523269534111023},{"id":"https://openalex.org/C48406656","wikidata":"https://www.wikidata.org/wiki/Q534112","display_name":"Martingale (probability theory)","level":2,"score":0.4666801691055298},{"id":"https://openalex.org/C43555835","wikidata":"https://www.wikidata.org/wiki/Q2300258","display_name":"Conditional probability distribution","level":2,"score":0.45561134815216064},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.4231802821159363},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4042391777038574},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33075106143951416},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.1777724027633667},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17133629322052002},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0860343873500824},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C196558001","wikidata":"https://www.wikidata.org/wiki/Q190132","display_name":"Turbulence","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/e27010002","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e27010002","pdf_url":"https://www.mdpi.com/1099-4300/27/1/2/pdf?version=1735051483","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmid:39851622","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/39851622","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:pubmedcentral.nih.gov:11764456","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/11764456","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC11764456/pdf/entropy-27-00002.pdf","source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy (Basel)","raw_type":"Text"},{"id":"pmh:oai:doaj.org/article:306fd8f878a04639ab5f5c60cef3450d","is_oa":false,"landing_page_url":"https://doaj.org/article/306fd8f878a04639ab5f5c60cef3450d","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 27, Iss 1, p 2 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/e27010002","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e27010002","pdf_url":"https://www.mdpi.com/1099-4300/27/1/2/pdf?version=1735051483","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/13","score":0.8100000023841858,"display_name":"Climate action"}],"awards":[{"id":"https://openalex.org/G1876783707","display_name":null,"funder_award_id":"W911NF-23-1-0118","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G567869125","display_name":null,"funder_award_id":"W911NF\u201023\u20101\u20100118","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G572140310","display_name":null,"funder_award_id":"N00014-24-1-2244","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G6742633021","display_name":null,"funder_award_id":"N00014-24-1-2244","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"}],"funders":[{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"},{"id":"https://openalex.org/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4405757841.pdf","grobid_xml":"https://content.openalex.org/works/W4405757841.grobid-xml"},"referenced_works_count":195,"referenced_works":["https://openalex.org/W91588129","https://openalex.org/W570977054","https://openalex.org/W585702508","https://openalex.org/W592485236","https://openalex.org/W650663117","https://openalex.org/W869363102","https://openalex.org/W913946616","https://openalex.org/W1410907832","https://openalex.org/W1494628843","https://openalex.org/W1509469724","https://openalex.org/W1516193414","https://openalex.org/W1523471994","https://openalex.org/W1523631876","https://openalex.org/W1539851785","https://openalex.org/W1579485993","https://openalex.org/W1596195796","https://openalex.org/W1597308977","https://openalex.org/W1625761746","https://openalex.org/W1647323343","https://openalex.org/W1776371429","https://openalex.org/W1907705813","https://openalex.org/W1955766749","https://openalex.org/W1964157577","https://openalex.org/W1964221133","https://openalex.org/W1966163772","https://openalex.org/W1971502565","https://openalex.org/W1972079349","https://openalex.org/W1973136150","https://openalex.org/W1975417422","https://openalex.org/W1976541894","https://openalex.org/W1976552644","https://openalex.org/W1977924985","https://openalex.org/W1978275259","https://openalex.org/W1980603880","https://openalex.org/W1981041832","https://openalex.org/W1983176089","https://openalex.org/W1985479415","https://openalex.org/W1987308763","https://openalex.org/W1988868967","https://openalex.org/W1990769357","https://openalex.org/W1999518711","https://openalex.org/W2005047575","https://openalex.org/W2005248345","https://openalex.org/W2015352008","https://openalex.org/W2016115539","https://openalex.org/W2016823018","https://openalex.org/W2017052080","https://openalex.org/W2018956455","https://openalex.org/W2021972235","https://openalex.org/W2025454051","https://openalex.org/W2026577854","https://openalex.org/W2028990747","https://openalex.org/W2029337327","https://openalex.org/W2029657087","https://openalex.org/W2031068659","https://openalex.org/W2045094459","https://openalex.org/W2049553322","https://openalex.org/W2061328952","https://openalex.org/W2061863349","https://openalex.org/W2062456242","https://openalex.org/W2068844053","https://openalex.org/W2068910417","https://openalex.org/W2072036814","https://openalex.org/W2072700524","https://openalex.org/W2074157958","https://openalex.org/W2076158645","https://openalex.org/W2076448662","https://openalex.org/W2077611006","https://openalex.org/W2079960826","https://openalex.org/W2081608955","https://openalex.org/W2083115723","https://openalex.org/W2083402998","https://openalex.org/W2088385764","https://openalex.org/W2090249381","https://openalex.org/W2090881117","https://openalex.org/W2094227853","https://openalex.org/W2101080583","https://openalex.org/W2101116262","https://openalex.org/W2101186745","https://openalex.org/W2104049095","https://openalex.org/W2104659821","https://openalex.org/W2105617589","https://openalex.org/W2107411554","https://openalex.org/W2109153769","https://openalex.org/W2111288282","https://openalex.org/W2118343917","https://openalex.org/W2124138287","https://openalex.org/W2124926041","https://openalex.org/W2127921550","https://openalex.org/W2128382396","https://openalex.org/W2128931495","https://openalex.org/W2133904834","https://openalex.org/W2134348739","https://openalex.org/W2134923619","https://openalex.org/W2134935769","https://openalex.org/W2141394518","https://openalex.org/W2141585124","https://openalex.org/W2143143555","https://openalex.org/W2144668858","https://openalex.org/W2146626950","https://openalex.org/W2147087715","https://openalex.org/W2150951085","https://openalex.org/W2152890166","https://openalex.org/W2152896489","https://openalex.org/W2153495538","https://openalex.org/W2157047632","https://openalex.org/W2160329836","https://openalex.org/W2171307019","https://openalex.org/W2179584279","https://openalex.org/W2179952483","https://openalex.org/W2180274418","https://openalex.org/W2239232218","https://openalex.org/W2318523722","https://openalex.org/W2342062156","https://openalex.org/W2343057691","https://openalex.org/W2346660758","https://openalex.org/W2397105798","https://openalex.org/W2402025460","https://openalex.org/W2473513981","https://openalex.org/W2507269661","https://openalex.org/W2519188913","https://openalex.org/W2527294977","https://openalex.org/W2560236645","https://openalex.org/W2586262377","https://openalex.org/W2624701197","https://openalex.org/W2739286039","https://openalex.org/W2755344066","https://openalex.org/W2767128663","https://openalex.org/W2769705890","https://openalex.org/W2789794913","https://openalex.org/W2790521266","https://openalex.org/W2801749227","https://openalex.org/W2810234128","https://openalex.org/W2885727792","https://openalex.org/W2940236260","https://openalex.org/W2962802251","https://openalex.org/W2962891488","https://openalex.org/W2962970455","https://openalex.org/W2963914861","https://openalex.org/W2964246490","https://openalex.org/W2964920143","https://openalex.org/W2969434393","https://openalex.org/W2972389908","https://openalex.org/W2997092692","https://openalex.org/W3006507139","https://openalex.org/W3009614366","https://openalex.org/W3010248150","https://openalex.org/W3015681226","https://openalex.org/W3021544678","https://openalex.org/W3034522316","https://openalex.org/W3098379020","https://openalex.org/W3098721375","https://openalex.org/W3101256565","https://openalex.org/W3101615282","https://openalex.org/W3103568683","https://openalex.org/W3125045238","https://openalex.org/W3158664135","https://openalex.org/W3159580798","https://openalex.org/W3173624651","https://openalex.org/W3189197029","https://openalex.org/W3201378086","https://openalex.org/W3217716227","https://openalex.org/W4200631298","https://openalex.org/W4210840459","https://openalex.org/W4211127940","https://openalex.org/W4211215604","https://openalex.org/W4214625488","https://openalex.org/W4230472026","https://openalex.org/W4231021340","https://openalex.org/W4231204432","https://openalex.org/W4231214543","https://openalex.org/W4238187298","https://openalex.org/W4239868095","https://openalex.org/W4240959780","https://openalex.org/W4242841269","https://openalex.org/W4247915326","https://openalex.org/W4248407260","https://openalex.org/W4250883246","https://openalex.org/W4251668531","https://openalex.org/W4254551825","https://openalex.org/W4282927304","https://openalex.org/W4302445759","https://openalex.org/W4362590479","https://openalex.org/W4376869050","https://openalex.org/W4383097042","https://openalex.org/W4385628969","https://openalex.org/W4386295691","https://openalex.org/W4388167314","https://openalex.org/W4391511921","https://openalex.org/W4400316765","https://openalex.org/W4400391957","https://openalex.org/W4401387955","https://openalex.org/W4405869221","https://openalex.org/W6681963429","https://openalex.org/W6765967938"],"related_works":["https://openalex.org/W3168953348","https://openalex.org/W2071970553","https://openalex.org/W2097781103","https://openalex.org/W4238858747","https://openalex.org/W1973163428","https://openalex.org/W2359480571","https://openalex.org/W2592623155","https://openalex.org/W2592465853","https://openalex.org/W2963081535","https://openalex.org/W1964286703"],"abstract_inverted_index":{"The":[0,180],"conditional":[1,66,107],"Gaussian":[2,28,67],"nonlinear":[3,11],"system":[4],"(CGNS)":[5],"is":[6,185],"a":[7,19,27,85,97,122,188],"broad":[8],"class":[9],"of":[10,21,64,73,92,105,144,173,182],"stochastic":[12],"dynamical":[13],"systems.":[14,166],"Given":[15],"the":[16,24,31,35,61,71,90,102,106,117,127,168,171,183],"trajectories":[17],"for":[18,60,136,140,156],"subset":[20],"state":[22,146],"variables,":[23],"remaining":[25],"follow":[26],"distribution.":[29],"Despite":[30],"conditionally":[32],"linear":[33],"structure,":[34],"CGNS":[36],"exhibits":[37],"strong":[38],"nonlinearity,":[39],"thus":[40],"capturing":[41],"many":[42],"non-Gaussian":[43],"characteristics":[44],"observed":[45],"in":[46,177],"nature":[47],"through":[48,112,187],"its":[49,65],"joint":[50],"and":[51,76,160,162,196],"marginal":[52],"distributions.":[53],"Desirably,":[54],"it":[55],"enjoys":[56],"closed":[57],"analytic":[58,138],"formulae":[59,139],"time":[62,103,113],"evolution":[63,104],"statistics,":[68],"which":[69],"facilitate":[70],"study":[72],"data":[74],"assimilation":[75],"other":[77],"related":[78],"topics.":[79],"In":[80],"this":[81],"paper,":[82],"we":[83],"develop":[84],"martingale-free":[86],"approach":[87,99,133,169],"to":[88,100,164],"improve":[89],"understanding":[91,172],"CGNSs.":[93],"This":[94,131],"methodology":[95],"provides":[96],"tractable":[98],"proving":[101],"statistics":[108],"by":[109],"deriving":[110],"results":[111],"discretization":[114,128],"schemes,":[115],"with":[116,148,193],"continuous-time":[118],"regime":[119],"obtained":[120],"via":[121],"formal":[123],"limiting":[124],"process":[125],"as":[126],"time-step":[129],"vanishes.":[130],"discretized":[132],"further":[134],"allows":[135],"developing":[137],"optimal":[141],"posterior":[142],"sampling":[143,175],"unobserved":[145],"variables":[147],"correlated":[149],"noise.":[150,199],"These":[151],"tools":[152],"are":[153],"particularly":[154],"valuable":[155],"studying":[157],"extreme":[158],"events":[159],"intermittency":[161],"apply":[163],"high-dimensional":[165],"Moreover,":[167],"improves":[170],"different":[174],"methods":[176],"characterizing":[178],"uncertainty.":[179],"effectiveness":[181],"framework":[184],"demonstrated":[186],"physics-constrained,":[189],"triad-interaction":[190],"climate":[191],"model":[192],"cubic":[194],"nonlinearity":[195],"state-dependent":[197],"cross-interacting":[198]},"counts_by_year":[],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}