{"id":"https://openalex.org/W4407295642","doi":"https://doi.org/10.3390/e27020179","title":"Occupation Times on the Legs of a Diffusion Spider","display_name":"Occupation Times on the Legs of a Diffusion Spider","publication_year":2025,"publication_date":"2025-02-08","ids":{"openalex":"https://openalex.org/W4407295642","doi":"https://doi.org/10.3390/e27020179","pmid":"https://pubmed.ncbi.nlm.nih.gov/40003176"},"language":"en","primary_location":{"id":"doi:10.3390/e27020179","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e27020179","pdf_url":null,"source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.3390/e27020179","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5047227884","display_name":"Paavo Salminen","orcid":"https://orcid.org/0000-0002-1968-4460"},"institutions":[{"id":"https://openalex.org/I130217899","display_name":"\u00c5bo Akademi University","ror":"https://ror.org/029pk6x14","country_code":"FI","type":"education","lineage":["https://openalex.org/I130217899"]}],"countries":["FI"],"is_corresponding":true,"raw_author_name":"Paavo Salminen","raw_affiliation_strings":["Faculty of Science and Engineering, \u00c5bo Akademi University, 20500 \u00c5bo, Finland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Science and Engineering, \u00c5bo Akademi University, 20500 \u00c5bo, Finland","institution_ids":["https://openalex.org/I130217899"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5043218925","display_name":"David Stenlund","orcid":"https://orcid.org/0000-0002-4697-8245"},"institutions":[{"id":"https://openalex.org/I141945490","display_name":"University of British Columbia","ror":"https://ror.org/03rmrcq20","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"David Stenlund","raw_affiliation_strings":["Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2, Canada"],"raw_orcid":"https://orcid.org/0000-0002-4697-8245","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2, Canada","institution_ids":["https://openalex.org/I141945490"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5047227884"],"corresponding_institution_ids":["https://openalex.org/I130217899"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.05237362,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"27","issue":"2","first_page":"179","last_page":"179"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9957000017166138,"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"}},"topics":[{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9957000017166138,"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/T10067","display_name":"Stochastic processes and financial applications","score":0.9840999841690063,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9817000031471252,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/spider","display_name":"Spider","score":0.8635129332542419},{"id":"https://openalex.org/keywords/bessel-function","display_name":"Bessel function","score":0.6814072132110596},{"id":"https://openalex.org/keywords/brownian-motion","display_name":"Brownian motion","score":0.6247919797897339},{"id":"https://openalex.org/keywords/laplace-transform","display_name":"Laplace transform","score":0.6208398342132568},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.574999213218689},{"id":"https://openalex.org/keywords/joint","display_name":"Joint (building)","score":0.568132221698761},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.5556010007858276},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3976617455482483},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.37165939807891846},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.23038113117218018},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1620366871356964},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.07150822877883911}],"concepts":[{"id":"https://openalex.org/C2780181586","wikidata":"https://www.wikidata.org/wiki/Q3966705","display_name":"Spider","level":2,"score":0.8635129332542419},{"id":"https://openalex.org/C107706756","wikidata":"https://www.wikidata.org/wiki/Q219637","display_name":"Bessel function","level":2,"score":0.6814072132110596},{"id":"https://openalex.org/C112401455","wikidata":"https://www.wikidata.org/wiki/Q178036","display_name":"Brownian motion","level":2,"score":0.6247919797897339},{"id":"https://openalex.org/C97937538","wikidata":"https://www.wikidata.org/wiki/Q199691","display_name":"Laplace transform","level":2,"score":0.6208398342132568},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.574999213218689},{"id":"https://openalex.org/C18555067","wikidata":"https://www.wikidata.org/wiki/Q8375051","display_name":"Joint (building)","level":2,"score":0.568132221698761},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.5556010007858276},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3976617455482483},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.37165939807891846},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.23038113117218018},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1620366871356964},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07150822877883911},{"id":"https://openalex.org/C170154142","wikidata":"https://www.wikidata.org/wiki/Q150737","display_name":"Architectural engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.3390/e27020179","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e27020179","pdf_url":null,"source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmid:40003176","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/40003176","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:pure.atira.dk:openaire/9df4a268-7353-4bc3-b440-9eee39de1ce8","is_oa":true,"landing_page_url":"https://research.abo.fi/en/publications/9df4a268-7353-4bc3-b440-9eee39de1ce8","pdf_url":null,"source":{"id":"https://openalex.org/S4406923060","display_name":"\u00c5bo Akademi University Research Portal","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Salminen, P & Stenlund, D 2025, 'Occupation times on the legs of a diffusion spider', Entropy, vol. 27, no. 2, 179. https://doi.org/10.3390/e27020179","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:circle.library.ubc.ca:2429/90429","is_oa":true,"landing_page_url":"http://hdl.handle.net/2429/90429","pdf_url":"https://open.library.ubc.ca/media/download/pdf/52383/1.0448135/3","source":{"id":"https://openalex.org/S4377196297","display_name":"cIRcle (University of British Columbia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I141945490","host_organization_name":"University of British Columbia","host_organization_lineage":["https://openalex.org/I141945490"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"pmh:oai:pubmedcentral.nih.gov:11854126","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/11854126","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC11854126/pdf/entropy-27-00179.pdf","source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy (Basel)","raw_type":"Text"},{"id":"pmh:oai:doaj.org/article:f3b844ed4d3d4094ac645c868b33a5e3","is_oa":false,"landing_page_url":"https://doaj.org/article/f3b844ed4d3d4094ac645c868b33a5e3","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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":"Entropy, Vol 27, Iss 2, p 179 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/e27020179","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e27020179","pdf_url":null,"source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322400","display_name":"Magnus Ehrnroothin S\u00e4\u00e4ti\u00f6","ror":"https://ror.org/02cdzet69"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W120758644","https://openalex.org/W173996936","https://openalex.org/W189861972","https://openalex.org/W1601026809","https://openalex.org/W1663426805","https://openalex.org/W1961358286","https://openalex.org/W1974450548","https://openalex.org/W1982339081","https://openalex.org/W1987771673","https://openalex.org/W1995358755","https://openalex.org/W2006735074","https://openalex.org/W2006859976","https://openalex.org/W2014163309","https://openalex.org/W2034649523","https://openalex.org/W2074285294","https://openalex.org/W2167963767","https://openalex.org/W2175190580","https://openalex.org/W2963113713","https://openalex.org/W2963812425","https://openalex.org/W2963826620","https://openalex.org/W2964030647","https://openalex.org/W2964281321","https://openalex.org/W3008720238","https://openalex.org/W3100748229","https://openalex.org/W3114013662","https://openalex.org/W3149447627","https://openalex.org/W3167056443","https://openalex.org/W3182279838","https://openalex.org/W4213415692","https://openalex.org/W4387213517","https://openalex.org/W4389078702","https://openalex.org/W4401179626","https://openalex.org/W6623988296","https://openalex.org/W6645894981","https://openalex.org/W6652068018","https://openalex.org/W6859402978","https://openalex.org/W6990570272"],"related_works":["https://openalex.org/W3116347567","https://openalex.org/W2049939404","https://openalex.org/W2054489131","https://openalex.org/W3113604371","https://openalex.org/W1519777678","https://openalex.org/W2989850994","https://openalex.org/W2034875467","https://openalex.org/W1823320495","https://openalex.org/W76811607","https://openalex.org/W2011121568"],"abstract_inverted_index":{"We":[0],"study":[1],"the":[2,9,22,26,43,57,61],"joint":[3,27,58],"moments":[4,59],"of":[5,11,25,41,60],"occupation":[6,62],"times":[7],"on":[8],"legs":[10],"a":[12,18,34,38,47],"diffusion":[13],"spider.":[14],"Specifically,":[15],"we":[16],"give":[17],"recursive":[19],"formula":[20,55],"for":[21,33,56],"Laplace":[23],"transform":[24],"moments,":[28],"which":[29,42],"extends":[30],"earlier":[31],"results":[32],"one-dimensional":[35],"diffusion.":[36],"For":[37],"Bessel":[39],"spider,":[40],"Brownian":[44],"spider":[45],"is":[46],"special":[48],"case,":[49],"our":[50],"approach":[51],"yields":[52],"an":[53],"explicit":[54],"times.":[63]},"counts_by_year":[],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}