{"id":"https://openalex.org/W7213500787","doi":"https://doi.org/10.48550/arxiv.2609.18229","title":"Finite-Dimensional Recursions for Small-Noise Expansions in Nonlinear Filtering","display_name":"Finite-Dimensional Recursions for Small-Noise Expansions in Nonlinear Filtering","publication_year":2026,"publication_date":"2026-09-16","ids":{"openalex":"https://openalex.org/W7213500787","doi":"https://doi.org/10.48550/arxiv.2609.18229"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.18229","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.18229","pdf_url":"https://arxiv.org/pdf/2609.18229","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.18229","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016032481","display_name":"Masahiro Kurisaki","orcid":"https://orcid.org/0000-0002-7701-2400","observed_orcids":["https://orcid.org/0000-0002-7701-2400"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Kurisaki, Masahiro","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5016032481"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10711","display_name":"Target Tracking and Data Fusion in Sensor Networks","score":0.9887999892234802,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10711","display_name":"Target Tracking and Data Fusion in Sensor Networks","score":0.9887999892234802,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.004800000227987766,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.001500000013038516,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/nonlinear-filtering","display_name":"nonlinear filtering","score":0.906000018119812},{"id":"https://openalex.org/keywords/kalman-bucy-filter","display_name":"Kalman-Bucy filter","score":0.8500000238418579},{"id":"https://openalex.org/keywords/fubini-s-theorem","display_name":"Fubini's theorem","score":0.890999972820282},{"id":"https://openalex.org/keywords/generalized-ito-formula","display_name":"generalized It\u00f4 formula","score":0.8069999814033508},{"id":"https://openalex.org/keywords/conditional-characteristic-function","display_name":"conditional characteristic function","score":0.9340000152587891},{"id":"https://openalex.org/keywords/conditional-expectation","display_name":"conditional expectation","score":0.7509999871253967}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7875999808311462},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6207000017166138},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.555899977684021},{"id":"https://openalex.org/C11683690","wikidata":"https://www.wikidata.org/wiki/Q752726","display_name":"Asymptotic expansion","level":2,"score":0.5149999856948853},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.4763999879360199},{"id":"https://openalex.org/C186215838","wikidata":"https://www.wikidata.org/wiki/Q772232","display_name":"Conditional expectation","level":2,"score":0.44519999623298645},{"id":"https://openalex.org/C158946198","wikidata":"https://www.wikidata.org/wiki/Q131187","display_name":"Taylor series","level":2,"score":0.3862000107765198},{"id":"https://openalex.org/C186080144","wikidata":"https://www.wikidata.org/wiki/Q358733","display_name":"Series expansion","level":2,"score":0.3650999963283539},{"id":"https://openalex.org/C36390408","wikidata":"https://www.wikidata.org/wiki/Q1163067","display_name":"Digital filter","level":3,"score":0.3407000005245209},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32679998874664307},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.28450000286102295},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.2833999991416931},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.2825999855995178},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.2669000029563904},{"id":"https://openalex.org/C148043351","wikidata":"https://www.wikidata.org/wiki/Q4456944","display_name":"Current (fluid)","level":2,"score":0.2632000148296356}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.18229","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.18229","pdf_url":"https://arxiv.org/pdf/2609.18229","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.18229","doi":"https://doi.org/10.48550/arxiv.2609.18229","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.18229","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.18229","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.18229","pdf_url":"https://arxiv.org/pdf/2609.18229","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G3090529436","display_name":null,"funder_award_id":"JP24KJ0667","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G6381513954","display_name":"\u5927\u898f\u6a21\u6642\u7a7a\u9593\u5f93\u5c5e\u6027\u30c7\u30fc\u30bf\u79d1\u5b66\u3078\u5411\u3051\u305f\u5148\u7aef\u7684\u78ba\u7387\u7d71\u8a08\u5b66\u306e\u65b0\u5c55\u958b","funder_award_id":"JPMJCR2115","funder_id":"https://openalex.org/F4320334789","funder_display_name":"Japan Science and Technology Agency"},{"id":"https://openalex.org/G7939374355","display_name":null,"funder_award_id":"JPMJCR2115","funder_id":"https://openalex.org/F4320338075","funder_display_name":"Core Research for Evolutional Science and Technology"}],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"},{"id":"https://openalex.org/F4320334789","display_name":"Japan Science and Technology Agency","ror":"https://ror.org/00097mb19"},{"id":"https://openalex.org/F4320335125","display_name":"RIKEN","ror":"https://ror.org/01sjwvz98"},{"id":"https://openalex.org/F4320338075","display_name":"Core Research for Evolutional Science and Technology","ror":"https://ror.org/00097mb19"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213500787.pdf","grobid_xml":"https://content.openalex.org/works/W7213500787.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W1749494163","https://openalex.org/W2003793708","https://openalex.org/W2007046555","https://openalex.org/W2009104157","https://openalex.org/W2018028661","https://openalex.org/W2034541289","https://openalex.org/W2050447955","https://openalex.org/W2058490559","https://openalex.org/W2083402998","https://openalex.org/W2094534023","https://openalex.org/W2098613108","https://openalex.org/W2105934661","https://openalex.org/W2105964352","https://openalex.org/W2136186628","https://openalex.org/W2150531296","https://openalex.org/W2539456164","https://openalex.org/W2890722078","https://openalex.org/W7118829399","https://openalex.org/W7201833121"],"related_works":["https://openalex.org/W7222676062","https://openalex.org/W4415334959","https://openalex.org/W4406931422","https://openalex.org/W7201833121","https://openalex.org/W4239849536","https://openalex.org/W2042350420","https://openalex.org/W1979073422","https://openalex.org/W2319032615","https://openalex.org/W2048872334","https://openalex.org/W1969825535"],"abstract_inverted_index":{"This":[0],"paper":[1],"provides":[2],"a":[3,11,42,98,116],"recursive":[4],"formula":[5,55],"for":[6,15],"computing":[7],"the":[8,22,28,38,46,58,66,78,83,87,105,120],"coefficients":[9],"in":[10,27],"small-system-noise":[12],"asymptotic":[13],"expansion":[14,64,106],"nonlinear":[16],"filtering.":[17],"The":[18],"expansion,":[19],"obtained":[20],"from":[21,107],"Kallianpur--Striebel":[23],"formula,":[24],"was":[25],"justified":[26],"author's":[29],"previous":[30],"work.":[31],"Our":[32],"main":[33],"contribution":[34],"is":[35],"to":[36,41,110],"reduce":[37],"coefficient":[39],"calculation":[40],"finite-dimensional":[43],"system":[44,79],"extending":[45],"Kalman--Bucy":[47],"filter":[48],"by":[49],"applying":[50],"Fubini's":[51],"theorem":[52],"and":[53,56,96,114],"Wick's":[54],"differentiating":[57],"resulting":[59],"terms.":[60],"For":[61],"each":[62],"fixed":[63],"order,":[65],"number":[67],"of":[68,93,119],"variables":[69],"grows":[70],"at":[71],"most":[72],"polynomially,":[73],"rather":[74],"than":[75],"exponentially,":[76],"with":[77],"dimension.":[80],"To":[81],"justify":[82],"construction,":[84],"we":[85],"define":[86],"required":[88],"non-adapted":[89],"integrals":[90],"as":[91],"limits":[92],"discrete":[94],"sums":[95],"establish":[97],"generalized":[99],"Ito":[100],"formula.":[101],"We":[102],"also":[103],"extend":[104],"conditional":[108,111],"expectations":[109],"characteristic":[112],"functions":[113],"provide":[115],"numerical":[117],"illustration":[118],"method.":[121]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-18T00:00:00"}
