{"id":"https://openalex.org/W3207918961","doi":"https://doi.org/10.1137/21m1401528","title":"Feynman--Kac Transform for Anomalous Processes","display_name":"Feynman--Kac Transform for Anomalous Processes","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3207918961","doi":"https://doi.org/10.1137/21m1401528","mag":"3207918961"},"language":"en","primary_location":{"id":"doi:10.1137/21m1401528","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1401528","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5077989905","display_name":"Zhen-Qing Chen","orcid":"https://orcid.org/0000-0001-7037-4030"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Zhen-Qing Chen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110039855","display_name":"Weihua Deng","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Weihua Deng","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-8573-012X","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5044165796","display_name":"Pengbo Xu","orcid":"https://orcid.org/0009-0001-3437-7426"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pengbo Xu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5077989905"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.6353,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.66770631,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"53","issue":"5","first_page":"6017","last_page":"6047"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T11513","display_name":"stochastic dynamics and bifurcation","score":0.9934999942779541,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.9750000238418579,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/subordinator","display_name":"Subordinator","score":0.9374980926513672},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7058844566345215},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.5648400783538818},{"id":"https://openalex.org/keywords/feynman-diagram","display_name":"Feynman diagram","score":0.5050700306892395},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.5034248232841492},{"id":"https://openalex.org/keywords/subject","display_name":"Subject (documents)","score":0.48415714502334595},{"id":"https://openalex.org/keywords/derivative","display_name":"Derivative (finance)","score":0.48161429166793823},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.457316130399704},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3489590287208557},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.33124101161956787},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.24301579594612122},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.19120654463768005},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13904160261154175},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13673430681228638},{"id":"https://openalex.org/keywords/l\u00e9vy-process","display_name":"L\u00e9vy process","score":0.10189956426620483},{"id":"https://openalex.org/keywords/library-science","display_name":"Library science","score":0.06995677947998047}],"concepts":[{"id":"https://openalex.org/C2781362121","wikidata":"https://www.wikidata.org/wiki/Q7631785","display_name":"Subordinator","level":3,"score":0.9374980926513672},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7058844566345215},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.5648400783538818},{"id":"https://openalex.org/C65574998","wikidata":"https://www.wikidata.org/wiki/Q386272","display_name":"Feynman diagram","level":2,"score":0.5050700306892395},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.5034248232841492},{"id":"https://openalex.org/C2777855551","wikidata":"https://www.wikidata.org/wiki/Q12310021","display_name":"Subject (documents)","level":2,"score":0.48415714502334595},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.48161429166793823},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.457316130399704},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3489590287208557},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.33124101161956787},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.24301579594612122},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.19120654463768005},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13904160261154175},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13673430681228638},{"id":"https://openalex.org/C88757350","wikidata":"https://www.wikidata.org/wiki/Q1557613","display_name":"L\u00e9vy process","level":2,"score":0.10189956426620483},{"id":"https://openalex.org/C161191863","wikidata":"https://www.wikidata.org/wiki/Q199655","display_name":"Library science","level":1,"score":0.06995677947998047},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/21m1401528","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1401528","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:/ir.lzu.edu.cn/:262010/480379","is_oa":false,"landing_page_url":"https://ir.lzu.edu.cn/handle/262010/480379","pdf_url":null,"source":{"id":"https://openalex.org/S4406923049","display_name":"Lanzhou University Institutional Repository","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":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5994574968","display_name":null,"funder_award_id":"12071195","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320306164","display_name":"Simons Foundation","ror":"https://ror.org/01cmst727"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W1495891378","https://openalex.org/W1975711585","https://openalex.org/W2003988116","https://openalex.org/W2020095085","https://openalex.org/W2026661822","https://openalex.org/W2035259748","https://openalex.org/W2035327124","https://openalex.org/W2045350842","https://openalex.org/W2048733177","https://openalex.org/W2098983106","https://openalex.org/W2108823069","https://openalex.org/W2111271983","https://openalex.org/W2182490673","https://openalex.org/W2266528679","https://openalex.org/W2476555123","https://openalex.org/W2576973016","https://openalex.org/W2592114611","https://openalex.org/W2783094414","https://openalex.org/W2806963689","https://openalex.org/W2962704971","https://openalex.org/W2963473848","https://openalex.org/W3022943542","https://openalex.org/W3041920824","https://openalex.org/W3094062926","https://openalex.org/W3099415531","https://openalex.org/W3101652349","https://openalex.org/W3102247295","https://openalex.org/W3103688219","https://openalex.org/W4242317941"],"related_works":["https://openalex.org/W2898068196","https://openalex.org/W2951166009","https://openalex.org/W4298306916","https://openalex.org/W4361867895","https://openalex.org/W1618442788","https://openalex.org/W1993482744","https://openalex.org/W2089892488","https://openalex.org/W2416906960","https://openalex.org/W2050580331","https://openalex.org/W3049300385"],"abstract_inverted_index":{"We":[0],"develop":[1],"a":[2,27,32,45,60,69,96,107,149],"new":[3],"approach":[4],"to":[5,95,123,133],"the":[6,9,42,91,119,135,154],"study":[7],"of":[8,44,52,78,138,142,163],"Feynman-Kac":[10],"transform":[11],"for":[12],"nonMarkov":[13],"anomalous":[14,143],"process":[15,30,110],"Y-t":[16],"=":[17,81],"X-Et":[18],"using":[19],"methods":[20],"from":[21],"stochastic":[22,161],"analysis,":[23],"where":[24,146],"X":[25,35,53,65,105,147],"is":[26,41,50,90,106,118,148],"strong":[28],"Markov":[29,109],"on":[31,64,111],"Lusin":[33],"space":[34,72],"and":[36,54,66,86,160],"{E-t,":[37],"t":[38],">=":[39],"0}":[40],"inverse":[43],"driftless":[46],"subordinator":[47],"S":[48],"that":[49,88,116,124],"independent":[51],"has":[55],"infinite":[56],"Levy":[57],"measure.":[58],"For":[59],"bounded":[61],"function":[62],"kappa":[63],"f":[67],"in":[68],"suitable":[70],"functional":[71],"over":[73],"X,":[74,112],"we":[75,113],"establish":[76],"regularity":[77],"u(t,":[79],"x)":[80],"E-x[exp(-":[82],"integral(t)(0)":[83],"kappa(Y-s)ds)":[84],"f(Y-t)]":[85],"show":[87,115],"it":[89],"unique":[92,120],"mild":[93],"solution":[94,122],"time":[97,125],"fractional":[98,126],"equation":[99],"with":[100],"initial":[101],"value":[102],"f.":[103],"When":[104],"symmetric":[108],"further":[114],"u":[117],"weak":[121],"equation.":[127],"The":[128],"main":[129],"results":[130],"are":[131],"applied":[132],"compute":[134],"probability":[136],"distribution":[137],"several":[139],"random":[140],"quantities":[141],"subdiffusion":[144],"Y":[145],"one-dimensional":[150],"Brownian":[151],"motion,":[152],"including":[153],"first":[155],"passage":[156],"time,":[157,159],"occupation":[158],"areas":[162],"Y.":[164]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}