{"id":"https://openalex.org/W7220920934","doi":"https://doi.org/10.48550/arxiv.2610.10252","title":"Limit theorems for one-dimensional diffusions: reflected, skew, sticky, skew-sticky, and snapping-out limits","display_name":"Limit theorems for one-dimensional diffusions: reflected, skew, sticky, skew-sticky, and snapping-out limits","publication_year":2026,"publication_date":"2026-10-07","ids":{"openalex":"https://openalex.org/W7220920934","doi":"https://doi.org/10.48550/arxiv.2610.10252"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.10252","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.10252","pdf_url":"https://arxiv.org/pdf/2610.10252","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/2610.10252","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5063520996","display_name":"Andrey Yurievich Pilipenko","orcid":"https://orcid.org/0000-0002-8786-1617","observed_orcids":["https://orcid.org/0000-0002-8786-1617"]},"institutions":[{"id":"https://openalex.org/I114457229","display_name":"University of Geneva","ror":"https://ror.org/01swzsf04","country_code":"CH","type":"education","lineage":["https://openalex.org/I114457229"]},{"id":"https://openalex.org/I149851306","display_name":"National Academy of Sciences of Ukraine","ror":"https://ror.org/00je4t102","country_code":"UA","type":"government","lineage":["https://openalex.org/I149851306"]},{"id":"https://openalex.org/I190444043","display_name":"Institute of Mathematics","ror":"https://ror.org/04q3mp532","country_code":"UA","type":"facility","lineage":["https://openalex.org/I149851306","https://openalex.org/I190444043"]}],"countries":["CH","UA"],"is_corresponding":false,"raw_author_name":"Pilipenko, Andrey","raw_affiliation_strings":["Institute of Mathematics of the National Academy of Sciences of Ukraine , Kyiv , Ukraine","Section of Mathematics , University of Geneva , Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics of the National Academy of Sciences of Ukraine , Kyiv , Ukraine","institution_ids":["https://openalex.org/I149851306","https://openalex.org/I190444043"]},{"raw_affiliation_string":"Section of Mathematics , University of Geneva , Switzerland","institution_ids":["https://openalex.org/I114457229"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5079619451","display_name":"Gilles Vilmart","orcid":"https://orcid.org/0000-0003-4593-1012","observed_orcids":["https://orcid.org/0000-0003-4593-1012"]},"institutions":[{"id":"https://openalex.org/I114457229","display_name":"University of Geneva","ror":"https://ror.org/01swzsf04","country_code":"CH","type":"education","lineage":["https://openalex.org/I114457229"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Vilmart, Gilles","raw_affiliation_strings":["Section of Mathematics , University of Geneva , Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Section of Mathematics , University of Geneva , Switzerland","institution_ids":["https://openalex.org/I114457229"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9702000021934509,"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":0.9702000021934509,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.011099999770522118,"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/T10067","display_name":"Stochastic processes and financial applications","score":0.005400000140070915,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/one-dimensional-diffusion","display_name":"one-dimensional diffusion","score":0.8840000033378601},{"id":"https://openalex.org/keywords/weak-convergence","display_name":"weak convergence","score":0.8769999742507935},{"id":"https://openalex.org/keywords/reflected-brownian-motion","display_name":"reflected Brownian motion","score":0.902999997138977},{"id":"https://openalex.org/keywords/skew-brownian-motion","display_name":"skew Brownian motion","score":0.9959999918937683},{"id":"https://openalex.org/keywords/homogenization","display_name":"homogenization","score":0.8309999704360962},{"id":"https://openalex.org/keywords/semipermeable-membranes","display_name":"semipermeable membranes","score":0.9710000157356262},{"id":"https://openalex.org/keywords/scale-function","display_name":"scale function","score":0.7559999823570251},{"id":"https://openalex.org/keywords/speed-measure","display_name":"speed measure","score":0.824999988079071},{"id":"https://openalex.org/keywords/time-change","display_name":"time change","score":0.6420000195503235},{"id":"https://openalex.org/keywords/scale-transformation","display_name":"scale transformation","score":0.7110000252723694},{"id":"https://openalex.org/keywords/boundary-conditions","display_name":"boundary conditions","score":0.5379999876022339}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8126000165939331},{"id":"https://openalex.org/C112401455","wikidata":"https://www.wikidata.org/wiki/Q178036","display_name":"Brownian motion","level":2,"score":0.673799991607666},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.5291000008583069},{"id":"https://openalex.org/C68710425","wikidata":"https://www.wikidata.org/wiki/Q5275442","display_name":"Diffusion process","level":3,"score":0.516700029373169},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5127999782562256},{"id":"https://openalex.org/C57945734","wikidata":"https://www.wikidata.org/wiki/Q7977941","display_name":"Weak convergence","level":3,"score":0.5084999799728394},{"id":"https://openalex.org/C43711488","wikidata":"https://www.wikidata.org/wiki/Q7534783","display_name":"Skew","level":2,"score":0.501800000667572},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.489300012588501},{"id":"https://openalex.org/C2778722038","wikidata":"https://www.wikidata.org/wiki/Q17030643","display_name":"Homogenization (climate)","level":3,"score":0.474700003862381},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.43070000410079956},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.42289999127388},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4221000075340271},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.40610000491142273},{"id":"https://openalex.org/C71287196","wikidata":"https://www.wikidata.org/wiki/Q847204","display_name":"Limit of a sequence","level":3,"score":0.40380001068115234},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.39329999685287476},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.387800008058548},{"id":"https://openalex.org/C53920899","wikidata":"https://www.wikidata.org/wiki/Q4976524","display_name":"Brownian excursion","level":5,"score":0.3718000054359436},{"id":"https://openalex.org/C193290586","wikidata":"https://www.wikidata.org/wiki/Q17022030","display_name":"Heavy traffic approximation","level":2,"score":0.3614000082015991},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.3571999967098236},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.35040000081062317},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.3319999873638153},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.3140000104904175},{"id":"https://openalex.org/C5871375","wikidata":"https://www.wikidata.org/wiki/Q1780715","display_name":"Compact convergence","level":4,"score":0.3068000078201294},{"id":"https://openalex.org/C60391097","wikidata":"https://www.wikidata.org/wiki/Q1056809","display_name":"Wiener process","level":2,"score":0.2921999990940094},{"id":"https://openalex.org/C14928880","wikidata":"https://www.wikidata.org/wiki/Q1512559","display_name":"Normal convergence","level":4,"score":0.28279998898506165},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.28209999203681946},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.26100000739097595},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.25589999556541443},{"id":"https://openalex.org/C95763700","wikidata":"https://www.wikidata.org/wiki/Q578985","display_name":"Convergence of random variables","level":3,"score":0.25519999861717224},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.2522999942302704}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.10252","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.10252","pdf_url":"https://arxiv.org/pdf/2610.10252","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.2610.10252","doi":"https://doi.org/10.48550/arxiv.2610.10252","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.10252","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-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.10252","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.10252","pdf_url":"https://arxiv.org/pdf/2610.10252","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/G1060292718","display_name":"Geometric and multiscale numerical methods for differential equations","funder_award_id":"214819","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G3091221485","display_name":"Stochastic dynamical systems with singularities","funder_award_id":"226875","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G4744247055","display_name":"Numerical Analysis","funder_award_id":"192129","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G628552264","display_name":null,"funder_award_id":"200020","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"}],"funders":[{"id":"https://openalex.org/F4320320924","display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","ror":"https://ror.org/00yjd3n13"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220920934.pdf","grobid_xml":"https://content.openalex.org/works/W7220920934.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W4415953812","https://openalex.org/W4416044869","https://openalex.org/W4417460443","https://openalex.org/W7117107081","https://openalex.org/W7126073766","https://openalex.org/W7214046344","https://openalex.org/W7220697883"],"related_works":["https://openalex.org/W2810602174","https://openalex.org/W1995228285","https://openalex.org/W2082024249","https://openalex.org/W2046691439","https://openalex.org/W4417460443","https://openalex.org/W2072633896","https://openalex.org/W7163552597","https://openalex.org/W2092817862","https://openalex.org/W4392060579","https://openalex.org/W7125956611"],"abstract_inverted_index":{"We":[0],"establish":[1],"general":[2],"conditions":[3,23],"for":[4,79],"the":[5,32,60,89],"weak":[6],"convergence":[7,54,61],"of":[8,36,45,62,113,120,130],"regular":[9,37],"one-dimensional":[10],"diffusion":[11,116],"processes":[12,92],"when":[13],"their":[14],"scale":[15,43],"functions,":[16,65],"speed":[17],"measures,":[18],"state":[19],"spaces":[20],"and":[21,42,67,97,106],"boundary":[22],"may":[24],"substantially":[25],"vary.":[26],"Our":[27],"approach":[28],"is":[29],"based":[30],"on":[31],"classical":[33],"It\u00f4--McKean":[34],"representation":[35,112],"diffusions":[38,80],"via":[39],"time":[40],"changes":[41],"transformations":[44],"a":[46,71,111,114,118,121],"single":[47,122],"Brownian":[48,99,104,123],"motion.":[49],"This":[50,109],"reduces":[51],"many":[52],"stochastic":[53],"problems":[55],"to":[56],"deterministic":[57],"questions":[58],"concerning":[59],"integrals,":[63],"monotone":[64],"compositions,":[66],"generalized":[68],"inverses.":[69],"As":[70],"main":[72],"application,":[73],"we":[74],"investigate":[75],"various":[76],"homogenization":[77],"regimes":[78],"in":[81],"media":[82],"with":[83],"closely":[84],"spaced":[85],"semipermeable":[86],"membranes,":[87],"where":[88],"resulting":[90],"limiting":[91],"include":[93],"not":[94],"only":[95],"reflected":[96],"skew":[98],"motions,":[100],"but":[101],"also":[102],"skew-sticky":[103],"motions":[105],"snapping-out":[107,115],"diffusions.":[108],"yields":[110],"as":[117],"function":[119],"motion,":[124],"without":[125],"introducing":[126],"an":[127],"auxiliary":[128],"sequence":[129],"independent":[131],"exponential":[132],"random":[133],"variables.":[134]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-09T00:00:00"}