{"id":"https://openalex.org/W7222005018","doi":"https://doi.org/10.48550/arxiv.2610.19233","title":"Moment-optimal Gamma approximation of Bessel Process exit times","display_name":"Moment-optimal Gamma approximation of Bessel Process exit times","publication_year":2026,"publication_date":"2026-10-13","ids":{"openalex":"https://openalex.org/W7222005018","doi":"https://doi.org/10.48550/arxiv.2610.19233"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.19233","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.19233","pdf_url":"https://arxiv.org/pdf/2610.19233","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/2610.19233","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036925897","display_name":"Steven P. Clark","orcid":"https://orcid.org/0000-0002-9075-410X","observed_orcids":["https://orcid.org/0000-0002-9075-410X"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Clark, Steven P.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5036925897"],"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/T11191","display_name":"Mathematical functions and polynomials","score":0.9136000275611877,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11191","display_name":"Mathematical functions and polynomials","score":0.9136000275611877,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11716","display_name":"Random Matrices and Applications","score":0.020400000736117363,"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"}},{"id":"https://openalex.org/T13500","display_name":"Probability and Statistical Research","score":0.014700000174343586,"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/bessel-processes","display_name":"Bessel processes","score":0.8799999952316284},{"id":"https://openalex.org/keywords/first-hitting-time","display_name":"first hitting time","score":0.8579999804496765},{"id":"https://openalex.org/keywords/moment-problem","display_name":"moment problem","score":0.4390000104904175},{"id":"https://openalex.org/keywords/cumulant-matching","display_name":"cumulant matching","score":0.7570000290870667},{"id":"https://openalex.org/keywords/exponential-representation","display_name":"exponential representation","score":0.5640000104904175},{"id":"https://openalex.org/keywords/laplace-transform","display_name":"Laplace transform","score":0.6499999761581421},{"id":"https://openalex.org/keywords/gaussian-quadrature","display_name":"Gaussian quadrature","score":0.7990000247955322},{"id":"https://openalex.org/keywords/geometric-convergence","display_name":"geometric convergence","score":0.625},{"id":"https://openalex.org/keywords/exit-time-distribution","display_name":"exit time distribution","score":0.5730000138282776}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8287000060081482},{"id":"https://openalex.org/C107706756","wikidata":"https://www.wikidata.org/wiki/Q219637","display_name":"Bessel function","level":2,"score":0.7368000149726868},{"id":"https://openalex.org/C39613435","wikidata":"https://www.wikidata.org/wiki/Q846677","display_name":"Remainder","level":2,"score":0.6809999942779541},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6312999725341797},{"id":"https://openalex.org/C97937538","wikidata":"https://www.wikidata.org/wiki/Q199691","display_name":"Laplace transform","level":2,"score":0.6233999729156494},{"id":"https://openalex.org/C17137986","wikidata":"https://www.wikidata.org/wiki/Q215067","display_name":"Orthogonality","level":2,"score":0.5889000296592712},{"id":"https://openalex.org/C179117685","wikidata":"https://www.wikidata.org/wiki/Q328998","display_name":"Complex plane","level":2,"score":0.531000018119812},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.5026999711990356},{"id":"https://openalex.org/C45347329","wikidata":"https://www.wikidata.org/wiki/Q5166604","display_name":"Convolution (computer science)","level":3,"score":0.4869999885559082},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.4713999927043915},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.4708000123500824},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.4260999858379364},{"id":"https://openalex.org/C118532472","wikidata":"https://www.wikidata.org/wiki/Q4896405","display_name":"Bessel process","level":5,"score":0.4237000048160553},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.3864000141620636},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.36250001192092896},{"id":"https://openalex.org/C126875415","wikidata":"https://www.wikidata.org/wiki/Q203425","display_name":"Unit circle","level":2,"score":0.3531000018119812},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.34470000863075256},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.3334999978542328},{"id":"https://openalex.org/C60455284","wikidata":"https://www.wikidata.org/wiki/Q2162701","display_name":"Inverse Laplace transform","level":3,"score":0.33340001106262207},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.3310000002384186},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.3197999894618988},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.30300000309944153},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.28949999809265137},{"id":"https://openalex.org/C167196314","wikidata":"https://www.wikidata.org/wiki/Q767680","display_name":"Gaussian quadrature","level":4,"score":0.2879999876022339},{"id":"https://openalex.org/C2777630202","wikidata":"https://www.wikidata.org/wiki/Q5527840","display_name":"Gaussian measure","level":3,"score":0.2831000089645386},{"id":"https://openalex.org/C201292218","wikidata":"https://www.wikidata.org/wiki/Q740970","display_name":"Recurrence relation","level":2,"score":0.27810001373291016},{"id":"https://openalex.org/C48490523","wikidata":"https://www.wikidata.org/wiki/Q371631","display_name":"Jacobi polynomials","level":3,"score":0.26930001378059387},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.2612000107765198},{"id":"https://openalex.org/C113285462","wikidata":"https://www.wikidata.org/wiki/Q856103","display_name":"Methods of contour integration","level":2,"score":0.26109999418258667},{"id":"https://openalex.org/C77246614","wikidata":"https://www.wikidata.org/wiki/Q1409400","display_name":"Gramian matrix","level":3,"score":0.2597000002861023},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.251800000667572}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.19233","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.19233","pdf_url":"https://arxiv.org/pdf/2610.19233","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.2610.19233","doi":"https://doi.org/10.48550/arxiv.2610.19233","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.19233","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:2610.19233","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.19233","pdf_url":"https://arxiv.org/pdf/2610.19233","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":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7222005018.pdf","grobid_xml":"https://content.openalex.org/works/W7222005018.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W2743662731"],"related_works":["https://openalex.org/W2769802109","https://openalex.org/W3167263014","https://openalex.org/W3161748271","https://openalex.org/W7096545774","https://openalex.org/W1560681088","https://openalex.org/W1988731743","https://openalex.org/W1991572054","https://openalex.org/W1486434834","https://openalex.org/W4396219263","https://openalex.org/W7029681421"],"abstract_inverted_index":{"We":[0],"construct":[1],"finite":[2],"Gamma":[3,55,109],"convolutions":[4],"approximating":[5],"the":[6,21,27,38,60,64,82,97,102,123],"first":[7,61],"hitting":[8],"time":[9],"of":[10,16,31,41,81,88,96,122],"$1$":[11],"by":[12,36],"a":[13,42,89],"Bessel":[14],"process":[15],"index":[17],"$\u03bd>-1$":[18],"started":[19],"at":[20],"origin.":[22],"The":[23,105],"scale":[24],"measure":[25],"in":[26,68],"classical":[28],"exponential":[29],"representation":[30],"this":[32,69],"law":[33],"is":[34],"obtained":[35],"squaring":[37],"positive":[39],"half":[40],"dilated":[43],"modified":[44],"Lommel":[45],"polynomial":[46],"orthogonality":[47],"measure.":[48],"Its":[49],"Jacobi":[50],"recurrence":[51],"yields":[52],"an":[53,72],"$N$-factor":[54],"convolution":[56],"that":[57],"uniquely":[58],"matches":[59],"$2N$":[62],"cumulants,":[63],"maximal":[65],"number":[66],"attainable":[67],"class.":[70],"From":[71],"exact":[73],"Gaussian":[74],"quadrature":[75],"remainder":[76],"we":[77],"derive":[78],"supergeometric":[79],"convergence":[80,95],"Laplace":[83,114],"transforms":[84,115],"on":[85,101],"compact":[86],"subsets":[87],"common":[90],"slit":[91],"plane":[92],"and":[93,112,116],"geometric":[94],"distribution":[98],"functions":[99],"uniformly":[100],"real":[103],"line.":[104],"approximants":[106],"have":[107],"total":[108],"shape":[110],"$N(N+\u03bd+1)$,":[111],"their":[113],"negative":[117],"moments":[118],"decrease":[119],"to":[120],"those":[121],"exit":[124],"law.":[125]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-16T00:00:00"}