{"id":"https://openalex.org/W2080153675","doi":"https://doi.org/10.1137/050622651","title":"Analysis of an Inverse First Passage Problem from Risk Management","display_name":"Analysis of an Inverse First Passage Problem from Risk Management","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2080153675","doi":"https://doi.org/10.1137/050622651","mag":"2080153675"},"language":"en","primary_location":{"id":"doi:10.1137/050622651","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050622651","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/A5052125406","display_name":"Lan Cheng","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lan Cheng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087971771","display_name":"Xinfu Chen","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xinfu Chen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065232026","display_name":"John Chadam","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"John Chadam","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5061487757","display_name":"David Saunders","orcid":"https://orcid.org/0000-0002-0870-6644"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"David Saunders","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0119,"has_fulltext":false,"cited_by_count":34,"citation_normalized_percentile":{"value":0.77119505,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"38","issue":"3","first_page":"845","last_page":"873"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T10067","display_name":"Stochastic processes and financial applications","score":0.9966999888420105,"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":0.9950000047683716,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8705192804336548},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.7492599487304688},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.6517335176467896},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.6142755746841431},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.5818967223167419},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5651822686195374},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5498839616775513},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5211055874824524},{"id":"https://openalex.org/keywords/first-hitting-time-model","display_name":"First-hitting-time model","score":0.4377230405807495},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.42246323823928833},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.42055752873420715},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.4166487455368042},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3230878710746765},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09473311901092529},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07497110962867737}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8705192804336548},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.7492599487304688},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.6517335176467896},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.6142755746841431},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.5818967223167419},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5651822686195374},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5498839616775513},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5211055874824524},{"id":"https://openalex.org/C186659197","wikidata":"https://www.wikidata.org/wiki/Q5452195","display_name":"First-hitting-time model","level":2,"score":0.4377230405807495},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.42246323823928833},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.42055752873420715},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.4166487455368042},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3230878710746765},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09473311901092529},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07497110962867737},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/050622651","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050622651","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:CiteSeerX.psu:10.1.1.414.9312","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.414.9312","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.pitt.edu/~chadam/papers/4DefBarrTheo19V05.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2868819213","display_name":"Numerical Techniques for Stochastic Partial Differential Equations with Non-Gaussian Noise","funder_award_id":"0310656","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7739314362","display_name":"Free Boundary Problems and Reaction-Diffusion Systems","funder_award_id":"0203991","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W61996051","https://openalex.org/W310937301","https://openalex.org/W1518792628","https://openalex.org/W1533819021","https://openalex.org/W1580561995","https://openalex.org/W1602967628","https://openalex.org/W2028801808","https://openalex.org/W2032316144","https://openalex.org/W2042058073","https://openalex.org/W2105973145","https://openalex.org/W2141436719","https://openalex.org/W2148474709","https://openalex.org/W3021722416","https://openalex.org/W3123848600","https://openalex.org/W3125196838","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W571281153","https://openalex.org/W2949403936","https://openalex.org/W3023806604","https://openalex.org/W2952139525","https://openalex.org/W4301247218","https://openalex.org/W2129818458","https://openalex.org/W1549756090","https://openalex.org/W3155039083","https://openalex.org/W1543136835","https://openalex.org/W4210375670"],"abstract_inverted_index":{"We":[0,64,77],"study":[1],"the":[2,34,41,58,66,80,85,101],"following":[3],"\u201cinverse":[4],"first":[5,35,60],"passage":[6,61],"time\u201d":[7],"problem.":[8,63,76],"Given":[9],"a":[10,15,24,50,71],"diffusion":[11],"process":[12],"$X_{t}$":[13,39],"and":[14,68,91],"probability":[16],"distribution":[17],"q":[18],"on":[19],"$[0,\\infty)$,":[20],"does":[21],"there":[22],"exist":[23],"boundary":[25,47,86],"$b(t)$":[26],"such":[27],"that":[28],"$q(t)=\\mathbb{P}[\\tau\\leq":[29],"t]$,":[30],"where":[31],"\u03c4":[32],"is":[33,55],"hitting":[36],"time":[37,62,82],"of":[38,70,84],"to":[40,74],"time\u2010dependent":[42],"level":[43],"$b(t)$?":[44],"A":[45],"free":[46],"problem":[48],"for":[49],"parabolic":[51],"partial":[52],"differential":[53],"operator":[54],"associated":[56],"with":[57],"inverse":[59],"prove":[65],"existence":[67],"uniqueness":[69],"viscosity":[72],"solution":[73],"this":[75],"also":[78],"investigate":[79],"small":[81],"behavior":[83],"$b(t)$,":[87],"presenting":[88],"both":[89],"upper":[90],"lower":[92],"bounds.":[93],"Finally,":[94],"we":[95],"derive":[96],"some":[97],"integral":[98],"equations":[99],"characterizing":[100],"boundary.":[102]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}