{"id":"https://openalex.org/W7214987965","doi":"https://doi.org/10.48550/arxiv.2609.37805","title":"Markov property for systems driven by the Brownian sheet","display_name":"Markov property for systems driven by the Brownian sheet","publication_year":2026,"publication_date":"2026-09-29","ids":{"openalex":"https://openalex.org/W7214987965","doi":"https://doi.org/10.48550/arxiv.2609.37805"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.37805","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.37805","pdf_url":"https://arxiv.org/pdf/2609.37805","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/2609.37805","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5083592351","display_name":"Nacira Agram","orcid":"https://orcid.org/0000-0003-1662-0215","observed_orcids":["https://orcid.org/0000-0003-1662-0215"]},"institutions":[{"id":"https://openalex.org/I4405259960","display_name":"Digital Futures","ror":"https://ror.org/02ztymy03","country_code":"SE","type":"facility","lineage":["https://openalex.org/I161593684","https://openalex.org/I2800664555","https://openalex.org/I4405259960","https://openalex.org/I86987016"]},{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Agram, Nacira","raw_affiliation_strings":["Department of Mathematics , KTH Royal Institute of Technology and Digital Futures , 100 44 , Stockholm , Sweden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , KTH Royal Institute of Technology and Digital Futures , 100 44 , Stockholm , Sweden","institution_ids":["https://openalex.org/I4405259960","https://openalex.org/I86987016"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5104384334","display_name":"Bernt \u00d8ksendal","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I184942183","display_name":"University of Oslo","ror":"https://ror.org/01xtthb56","country_code":"NO","type":"education","lineage":["https://openalex.org/I184942183"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"\u00d8ksendal, Bernt","raw_affiliation_strings":["Department of Mathematics , University of Oslo , Norway"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , University of Oslo , Norway","institution_ids":["https://openalex.org/I184942183"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079213730","display_name":"Frank Proske","orcid":"https://orcid.org/0000-0002-0463-0726","observed_orcids":["https://orcid.org/0000-0002-0463-0726"]},"institutions":[{"id":"https://openalex.org/I184942183","display_name":"University of Oslo","ror":"https://ror.org/01xtthb56","country_code":"NO","type":"education","lineage":["https://openalex.org/I184942183"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"Proske, Frank","raw_affiliation_strings":["Department of Mathematics , University of Oslo , Norway"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , University of Oslo , Norway","institution_ids":["https://openalex.org/I184942183"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001412990","display_name":"Olena A. Tymoshenko","orcid":"https://orcid.org/0000-0003-1885-7275","observed_orcids":["https://orcid.org/0000-0003-1885-7275"]},"institutions":[{"id":"https://openalex.org/I184942183","display_name":"University of Oslo","ror":"https://ror.org/01xtthb56","country_code":"NO","type":"education","lineage":["https://openalex.org/I184942183"]},{"id":"https://openalex.org/I202483615","display_name":"National Technical University of Ukraine \u201cIgor Sikorsky Kyiv Polytechnic Institute\u201d","ror":"https://ror.org/00syn5v21","country_code":"UA","type":"education","lineage":["https://openalex.org/I202483615"]}],"countries":["NO","UA"],"is_corresponding":false,"raw_author_name":"Tymoshenko, Olena","raw_affiliation_strings":["Department of Mathematical Analysis and Probability Theory , Igor Sikorsky Kyiv Polytechnic Institute , Ukraine","Department of Mathematics , University of Oslo , Norway"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Analysis and Probability Theory , Igor Sikorsky Kyiv Polytechnic Institute , Ukraine","institution_ids":["https://openalex.org/I202483615"]},{"raw_affiliation_string":"Department of Mathematics , University of Oslo , Norway","institution_ids":["https://openalex.org/I184942183"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"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/T10067","display_name":"Stochastic processes and financial applications","score":0.9868000149726868,"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"}},"topics":[{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9868000149726868,"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"}},{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.010099999606609344,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13500","display_name":"Probability and Statistical Research","score":0.0003000000142492354,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/brownian-sheet","display_name":"Brownian sheet","score":0.8759999871253967},{"id":"https://openalex.org/keywords/markov-property","display_name":"Markov property","score":0.9779999852180481},{"id":"https://openalex.org/keywords/girsanov-theorem","display_name":"Girsanov theorem","score":0.8610000014305115},{"id":"https://openalex.org/keywords/boundary-data","display_name":"boundary data","score":0.7039999961853027}],"concepts":[{"id":"https://openalex.org/C112401455","wikidata":"https://www.wikidata.org/wiki/Q178036","display_name":"Brownian motion","level":2,"score":0.6696000099182129},{"id":"https://openalex.org/C104824951","wikidata":"https://www.wikidata.org/wiki/Q830124","display_name":"Girsanov theorem","level":3,"score":0.6556000113487244},{"id":"https://openalex.org/C48406656","wikidata":"https://www.wikidata.org/wiki/Q534112","display_name":"Martingale (probability theory)","level":2,"score":0.6528000235557556},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.621999979019165},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.5612000226974487},{"id":"https://openalex.org/C162344956","wikidata":"https://www.wikidata.org/wiki/Q6777133","display_name":"Martingale representation theorem","level":5,"score":0.5322999954223633},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.5274999737739563},{"id":"https://openalex.org/C189973286","wikidata":"https://www.wikidata.org/wiki/Q176695","display_name":"Markov property","level":4,"score":0.5248000025749207},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.47920000553131104},{"id":"https://openalex.org/C78651780","wikidata":"https://www.wikidata.org/wiki/Q628309","display_name":"Brownian bridge","level":3,"score":0.4616999924182892},{"id":"https://openalex.org/C53920899","wikidata":"https://www.wikidata.org/wiki/Q4976524","display_name":"Brownian excursion","level":5,"score":0.45100000500679016},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.4101000130176544},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3901999890804291},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3677999973297119},{"id":"https://openalex.org/C58435881","wikidata":"https://www.wikidata.org/wiki/Q1868500","display_name":"Local martingale","level":3,"score":0.335099995136261},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.3287999927997589},{"id":"https://openalex.org/C68710425","wikidata":"https://www.wikidata.org/wiki/Q5275442","display_name":"Diffusion process","level":3,"score":0.32710000872612},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.322299987077713},{"id":"https://openalex.org/C116779161","wikidata":"https://www.wikidata.org/wiki/Q7307228","display_name":"Reflected Brownian motion","level":5,"score":0.2773999869823456},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.26339998841285706},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.2623000144958496},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.26170000433921814}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.37805","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.37805","pdf_url":"https://arxiv.org/pdf/2609.37805","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.2609.37805","doi":"https://doi.org/10.48550/arxiv.2609.37805","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.37805","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.37805","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.37805","pdf_url":"https://arxiv.org/pdf/2609.37805","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/G3524232687","display_name":"Advances in Stochastic Control Theory and Applications","funder_award_id":"2020-04697","funder_id":"https://openalex.org/F4320322581","funder_display_name":"Vetenskapsr\u00e5det"}],"funders":[{"id":"https://openalex.org/F4320322581","display_name":"Vetenskapsr\u00e5det","ror":"https://ror.org/03zttf063"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214987965.pdf","grobid_xml":"https://content.openalex.org/works/W7214987965.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2087627067","https://openalex.org/W2375400201","https://openalex.org/W2376511988","https://openalex.org/W6989157934","https://openalex.org/W1979389125","https://openalex.org/W1531136521","https://openalex.org/W2000279207","https://openalex.org/W2008356708","https://openalex.org/W1983503655","https://openalex.org/W2287740214"],"abstract_inverted_index":{"We":[0,55,109],"study":[1],"stochastic":[2],"systems":[3],"driven":[4],"by":[5,34,42,79,92],"a":[6,11,28,68,112],"Brownian":[7,86,101,106,113],"sheet":[8,102,107,114],"and":[9,49,103,117],"formulate":[10],"Markov":[12,70],"property":[13,71,98],"adapted":[14],"to":[15,74,120],"their":[16],"two-parameter":[17],"structure.":[18],"For":[19],"time-space":[20],"homogeneous":[21],"It\u00f4":[22],"sheets,":[23],"the":[24,35,43,47,59,64,75,80,85,95,100],"future":[25],"evolution":[26],"from":[27,53],"point":[29],"$(t,x)$":[30],"is":[31,90],"not":[32],"determined":[33],"single":[36],"value":[37],"$Y(t,x)$":[38],"alone,":[39],"but":[40],"also":[41,110],"boundary":[44],"data":[45],"along":[46],"horizontal":[48],"vertical":[50],"edges":[51],"issuing":[52],"$(t,x)$.":[54],"therefore":[56],"show":[57],"that":[58],"enlarged":[60],"state":[61],"consisting":[62],"of":[63,84],"triple":[65],"$(Y,D_1Y,D_2Y)$":[66],"satisfies":[67],"natural":[69],"with":[72],"respect":[73],"past":[76],"sigma-algebra":[77],"generated":[78],"two":[81],"coordinate":[82],"histories":[83],"sheet.":[87],"The":[88],"result":[89],"illustrated":[91],"examples":[93],"showing":[94],"strong":[96],"martingale":[97],"for":[99,104],"simple":[105],"systems.":[108],"recall":[111],"Girsanov":[115],"theorem":[116],"use":[118],"it":[119],"treat":[121],"drifted":[122],"sheets.":[123]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-10-01T00:00:00"}