{"id":"https://openalex.org/W7164410342","doi":"https://doi.org/10.48550/arxiv.2606.11994","title":"Variation and Hausdorff dimension of fractional Wiener-Weierstrass bridges","display_name":"Variation and Hausdorff dimension of fractional Wiener-Weierstrass bridges","publication_year":2026,"publication_date":"2026-06-10","ids":{"openalex":"https://openalex.org/W7164410342","doi":"https://doi.org/10.48550/arxiv.2606.11994"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2606.11994","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2606.11994","pdf_url":"https://arxiv.org/pdf/2606.11994","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/2606.11994","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5034171587","display_name":"Alexander Schied","orcid":"https://orcid.org/0000-0003-0296-7701","observed_orcids":["https://orcid.org/0000-0003-0296-7701"]},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]},{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["CA","US"],"is_corresponding":false,"raw_author_name":"Schied, Alexander","raw_affiliation_strings":["Department of Mathematics , Stanford University","Department of Statistics and Actuarial Science , University of Waterloo"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Stanford University","institution_ids":["https://openalex.org/I97018004"]},{"raw_affiliation_string":"Department of Statistics and Actuarial Science , University of Waterloo","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5126851894","display_name":"Zhenyuan Zhang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]},{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["CA","US"],"is_corresponding":false,"raw_author_name":"Zhang, Zhenyuan","raw_affiliation_strings":["Department of Mathematics , Stanford University","Department of Statistics and Actuarial Science , University of Waterloo"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Stanford University","institution_ids":["https://openalex.org/I97018004"]},{"raw_affiliation_string":"Department of Statistics and Actuarial Science , University of Waterloo","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"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/T10067","display_name":"Stochastic processes and financial applications","score":0.29760000109672546,"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"}},"topics":[{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.29760000109672546,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.17270000278949738,"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/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.15929999947547913,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"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/weierstrass-function","display_name":"Weierstrass function","score":0.7870000004768372},{"id":"https://openalex.org/keywords/gaussian-processes","display_name":"Gaussian processes","score":0.8190000057220459},{"id":"https://openalex.org/keywords/sample-path-properties","display_name":"sample path properties","score":0.9129999876022339},{"id":"https://openalex.org/keywords/power-variation","display_name":"power variation","score":0.7789999842643738},{"id":"https://openalex.org/keywords/hausdorff-dimension","display_name":"Hausdorff dimension","score":0.9610000252723694},{"id":"https://openalex.org/keywords/hurst-exponent","display_name":"Hurst exponent","score":0.6660000085830688}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8274999856948853},{"id":"https://openalex.org/C78651780","wikidata":"https://www.wikidata.org/wiki/Q628309","display_name":"Brownian bridge","level":3,"score":0.5914000272750854},{"id":"https://openalex.org/C194198291","wikidata":"https://www.wikidata.org/wiki/Q565186","display_name":"Hausdorff dimension","level":2,"score":0.5799000263214111},{"id":"https://openalex.org/C108819105","wikidata":"https://www.wikidata.org/wiki/Q1143293","display_name":"Fractional Brownian motion","level":3,"score":0.5586000084877014},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5320000052452087},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5181000232696533},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.4909000098705292},{"id":"https://openalex.org/C112401455","wikidata":"https://www.wikidata.org/wiki/Q178036","display_name":"Brownian motion","level":2,"score":0.47519999742507935},{"id":"https://openalex.org/C118733216","wikidata":"https://www.wikidata.org/wiki/Q332504","display_name":"Absolute continuity","level":2,"score":0.43470001220703125},{"id":"https://openalex.org/C191399826","wikidata":"https://www.wikidata.org/wiki/Q326908","display_name":"Hausdorff space","level":2,"score":0.4311000108718872},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.39890000224113464},{"id":"https://openalex.org/C198531522","wikidata":"https://www.wikidata.org/wiki/Q485146","display_name":"Sample (material)","level":2,"score":0.3953999876976013},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.39010000228881836},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.3882000148296356},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.3675000071525574},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.3637000024318695},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.34700000286102295},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.3449000120162964},{"id":"https://openalex.org/C29001434","wikidata":"https://www.wikidata.org/wiki/Q8084","display_name":"Trigonometry","level":2,"score":0.3418000042438507},{"id":"https://openalex.org/C40636538","wikidata":"https://www.wikidata.org/wiki/Q81392","display_name":"Fractal","level":2,"score":0.33570000529289246},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.31299999356269836},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.30799999833106995},{"id":"https://openalex.org/C120362076","wikidata":"https://www.wikidata.org/wiki/Q1149336","display_name":"Trigonometric series","level":2,"score":0.30379998683929443},{"id":"https://openalex.org/C53920899","wikidata":"https://www.wikidata.org/wiki/Q4976524","display_name":"Brownian excursion","level":5,"score":0.29649999737739563},{"id":"https://openalex.org/C115311070","wikidata":"https://www.wikidata.org/wiki/Q5347255","display_name":"Effective dimension","level":3,"score":0.2824000120162964},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.28200000524520874},{"id":"https://openalex.org/C88871306","wikidata":"https://www.wikidata.org/wiki/Q7208287","display_name":"Point process","level":2,"score":0.27619999647140503},{"id":"https://openalex.org/C24084028","wikidata":"https://www.wikidata.org/wiki/Q7429781","display_name":"Scaling limit","level":3,"score":0.2615000009536743},{"id":"https://openalex.org/C71039073","wikidata":"https://www.wikidata.org/wiki/Q3439090","display_name":"Surface finish","level":2,"score":0.2596000134944916},{"id":"https://openalex.org/C178009071","wikidata":"https://www.wikidata.org/wiki/Q93344","display_name":"Trigonometric functions","level":2,"score":0.2549999952316284},{"id":"https://openalex.org/C65778772","wikidata":"https://www.wikidata.org/wiki/Q12345341","display_name":"Asymptotic distribution","level":3,"score":0.25209999084472656}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2606.11994","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2606.11994","pdf_url":"https://arxiv.org/pdf/2606.11994","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.2606.11994","doi":"https://doi.org/10.48550/arxiv.2606.11994","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.11994","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:2606.11994","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2606.11994","pdf_url":"https://arxiv.org/pdf/2606.11994","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/G4879637183","display_name":null,"funder_award_id":"RGPIN-2024-03761","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"}],"funders":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7164410342.pdf","grobid_xml":"https://content.openalex.org/works/W7164410342.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4404389307","https://openalex.org/W4390535986","https://openalex.org/W2038037248","https://openalex.org/W3086774245","https://openalex.org/W1599636542","https://openalex.org/W7154567802","https://openalex.org/W2080653347","https://openalex.org/W2746026490","https://openalex.org/W106606825","https://openalex.org/W1966460344"],"abstract_inverted_index":{"Fractional":[0],"Wiener--Weierstrass":[1],"bridges":[2],"are":[3,49],"a":[4,123],"class":[5],"of":[6,17,27,47,117],"Gaussian":[7],"processes":[8],"obtained":[9],"by":[10,21,121],"replacing":[11],"trigonometric":[12],"functions":[13,20],"in":[14,34,39,56,59,105],"the":[15,57,61,65,70,86,90,96,100,111,115,118,129],"construction":[16],"classical":[18],"Weierstrass":[19,62],"fractional":[22,67],"Brownian":[23,68],"bridges.":[24],"A":[25],"number":[26],"their":[28],"sample":[29,119],"path":[30],"properties":[31],"were":[32],"derived":[33],"Schied--Zhang":[35,106,126],"(2024,2026).":[36],"The":[37],"analysis":[38],"these":[40],"papers":[41],"left":[42],"several":[43],"open":[44],"questions,":[45],"most":[46],"which":[48,60],"addressed":[50],"here.":[51],"Specifically,":[52],"we":[53,94,109],"prove":[54],"that,":[55],"regime":[58],"mechanism":[63],"dominates":[64],"underlying":[66],"bridge,":[69],"limiting":[71],"$b$-adic":[72],"variation":[73],"coefficient":[74],"has":[75],"an":[76],"absolutely":[77],"continuous":[78],"distribution":[79],"and":[80,99],"is":[81],"therefore":[82],"genuinely":[83],"random.":[84],"At":[85],"critical":[87,101],"point":[88],"between":[89],"two":[91],"roughness":[92],"regimes,":[93],"establish":[95],"power-variation":[97],"formula":[98],"$\u03a6$-variation":[102],"limit":[103],"conjectured":[104],"(2024).":[107],"Finally,":[108],"derive":[110],"Hausdorff":[112],"dimension":[113],"for":[114,128],"graphs":[116],"paths":[120],"proving":[122],"conjecture":[124],"from":[125],"(2026)":[127],"missing":[130],"high-Hurst":[131],"case.":[132]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-06-12T00:00:00"}
