d430106851cd0bdd52d171fc2a1ae4e3  StaProLet_a2026v235p110714.pdf
042ef056124dee7b5c65be9f1408575436bb5072  StaProLet_a2026v235p110714.pdf
decbd5ee7ea957493a8cf2ae8feb73304cd208aa5ad9cc1c80667d9cbc3d207d  StaProLet_a2026v235p110714.pdf

Title:           Kac–Stroock type approximations for the Brownian motion from renewal processes
Subject:         Statistics and Probability Letters, 235 (2026) 110714. doi:10.1016/j.spl.2026.110714
Keywords:        Brownian motion,Renewal process,Weak convergence,Kac–Stroock approximations
Author:          Xavier Bardina
Creator:         Elsevier
Producer:        Acrobat Distiller 8.1.0 (Windows)
CreationDate:    Thu Mar 12 17:04:50 2026 CET
ModDate:         Mon Mar 16 13:59:30 2026 CET
Custom Metadata: yes
Metadata Stream: yes
Tagged:          yes
UserProperties:  no
Suspects:        no
Form:            none
JavaScript:      no
Pages:           5
Encrypted:       no
Page size:       544.252 x 742.677 pts
Page rot:        0
File size:       613199 bytes
Optimized:       yes
PDF version:     1.7


name                                 type              encoding         emb sub uni object ID
------------------------------------ ----------------- ---------------- --- --- --- ---------
FSWQQS+CharisSIL-Italic              Type 1            Builtin          yes yes yes    170  0
XGUPJE+CharisSIL                     CID TrueType      Identity-H       yes yes yes    174  0
DUCSBQ+CharisSIL-Bold                Type 1            Builtin          yes yes yes    180  0
LJGQWF+CharisSIL                     Type 1            Builtin          yes yes yes    184  0
AXUTNU+MSBM7                         Type 1            Builtin          yes yes yes    188  0
XVZVYO+LMRoman10-Regular             CID Type 0C       Identity-H       yes yes yes    192  0
OMYYIL+STIXMathCalligraphy-Regular   Type 1            Builtin          yes yes yes    198  0
XKEQYD+STIXMathExtensions-Regular    Type 1            Builtin          yes yes yes    202  0
NBCBHQ+STIXMath-Regular              Type 1            Builtin          yes yes yes    206  0
TVGGGO+Dingbats                      Type 1            Builtin          yes yes yes    210  0
VWTDPZ+STIXMath-Italic               Type 1            Builtin          yes yes yes    214  0
PFUYCM+t1-uni-regular                Type 1            Builtin          yes yes yes    218  0
AAAUKD+CharisSIL                     CID TrueType      Identity-H       yes yes yes    222  0
AAAAAD+CharisSIL                     CID TrueType      Identity-H       yes yes yes     30  0
VEVLHQ+CharisSIL-Italic              CID TrueType      Identity-H       yes yes yes     37  0
OYDKZY+STIXMathSans-Regular          Type 1            Builtin          yes yes yes     43  0
AAAALE+CharisSIL-Italic              CID TrueType      Identity-H       yes yes yes     47  0
HHNCYN+MSBM10                        Type 1            Builtin          yes yes yes     54  0
WHHDUM+STIXMathScript-Regular        Type 1            Builtin          yes yes yes     58  0


Jhove (Rel. 1.28.0, 2023-05-18)
 Date: 2026-03-26 04:10:30 CET
 RepresentationInformation: StaProLet_a2026v235p110714.pdf
  ReportingModule: PDF-hul, Rel. 1.12.4 (2023-03-16)
  LastModified: 2026-03-25 20:18:07 CET
  Size: 613199
  Format: PDF
  Version: 1.7
  Status: Well-Formed and valid
  SignatureMatches:
   PDF-hul
  MIMEtype: application/pdf
  Profile: Linearized PDF, Tagged PDF
  PDFMetadata: 
   Objects: 943
   FreeObjects: 1
   IncrementalUpdates: 1
   DocumentCatalog: 
    ViewerPreferences: 
     HideToolbar: false
     HideMenubar: false
     HideWindowUI: false
     FitWindow: false
     CenterWindow: false
     DisplayDocTitle: true
     NonFullScreenPageMode: UseNone
     Direction: L2R
     ViewArea: CropBox
     ViewClip: CropBox
     PrintArea: CropBox
     PageClip: CropBox
    PageLayout: SinglePage
    PageMode: UseOutlines
    Language: en-US
    Outlines: 
     Item: 
      Title: Kac–Stroock type approximations for the Brownian motion from renewal processes
      Children: 
       Item: 
        Title: Introduction
       Item: 
        Title: Statement and proof of the main result
       Item: 
        Title: Acknowledgments
       Item: 
        Title: Data availability
       Item: 
        Title: References
   Info: 
    Title: Kac Stroock type approximations for the Brownian motion from renewal processes
    Author: Xavier Bardina
    Subject: Statistics and Probability Letters, 235 (2026) 110714. doi:10.1016/j.spl.2026.110714
    Keywords: Brownian motion,Renewal process,Weak convergence,Kac Stroock approximations
    Creator: Elsevier
    Producer: Acrobat Distiller 8.1.0 (Windows)
    CreationDate: Thu Mar 12 17:04:50 CET 2026
    ModDate: Mon Mar 16 13:59:30 CET 2026
   ID: 0x2620b36098eea4e0867e28f5d90d4b67, 0x3c5c835c3e340a83e7365b0f9a68b89d
   Filters: 
    FilterPipeline: FlateDecode
   Fonts: 
    Type0: 
     Font: 
      BaseFont: XVZVYO+LMRoman10-Regular
      Encoding: Identity-H
      ToUnicode: true
     Font: 
      BaseFont: VEVLHQ+CharisSIL-Italic
      Encoding: Identity-H
      ToUnicode: true
     Font: 
      BaseFont: XGUPJE+CharisSIL
      Encoding: Identity-H
      ToUnicode: true
     Font: 
      BaseFont: AAAUKD+CharisSIL
      Encoding: Identity-H
      ToUnicode: true
     Font: 
      BaseFont: AAAAAD+CharisSIL
      Encoding: Identity-H
      ToUnicode: true
     Font: 
      BaseFont: AAAALE+CharisSIL-Italic
      Encoding: Identity-H
      ToUnicode: true
    Type1: 
     Font: 
      BaseFont: OMYYIL+STIXMathCalligraphy-Regular
      FontSubset: true
      FirstChar: 67
      LastChar: 202
      FontDescriptor: 
       FontName: OMYYIL+STIXMathCalligraphy-Regular
       Flags: Symbolic
       FontBBox: -53, -455, 1965, 2157
       FontFile: true
      ToUnicode: true
     Font: 
      BaseFont: XKEQYD+STIXMathExtensions-Regular
      FontSubset: true
      FirstChar: 0
      LastChar: 249
      FontDescriptor: 
       FontName: XKEQYD+STIXMathExtensions-Regular
       Flags: Symbolic
       FontBBox: 15, -3009, 1503, 959
       FontFile: true
      ToUnicode: true
     Font: 
      BaseFont: FSWQQS+CharisSIL-Italic
      FontSubset: true
      FirstChar: 44
      LastChar: 242
      FontDescriptor: 
       FontName: FSWQQS+CharisSIL-Italic
       Flags: Symbolic
       FontBBox: -1467, -1092, 6262, 2600
       FontFile: true
      ToUnicode: true
     Font: 
      BaseFont: OYDKZY+STIXMathSans-Regular
      FontSubset: true
      FirstChar: 44
      LastChar: 173
      FontDescriptor: 
       FontName: OYDKZY+STIXMathSans-Regular
       Flags: Symbolic
       FontBBox: -124, -232, 1151, 819
       FontFile: true
      ToUnicode: true
     Font: 
      BaseFont: NBCBHQ+STIXMath-Regular
      FontSubset: true
      FirstChar: 42
      LastChar: 228
      FontDescriptor: 
       FontName: NBCBHQ+STIXMath-Regular
       Flags: Symbolic
       FontBBox: -970, -341, 1096, 1023
       FontFile: true
      ToUnicode: true
     Font: 
      BaseFont: TVGGGO+Dingbats
      FontSubset: true
      FirstChar: 73
      LastChar: 73
      FontDescriptor: 
       FontName: TVGGGO+Dingbats
       Flags: Symbolic
       FontBBox: -1, -143, 981, 819
       FontFile: true
      ToUnicode: true
     Font: 
      BaseFont: DUCSBQ+CharisSIL-Bold
      FontSubset: true
      FirstChar: 46
      LastChar: 121
      FontDescriptor: 
       FontName: DUCSBQ+CharisSIL-Bold
       Flags: Symbolic
       FontBBox: -1475, -1092, 6144, 2600
       FontFile: true
      ToUnicode: true
     Font: 
      BaseFont: VWTDPZ+STIXMath-Italic
      FontSubset: true
      FirstChar: 8
      LastChar: 207
      FontDescriptor: 
       FontName: VWTDPZ+STIXMath-Italic
       Flags: Symbolic
       FontBBox: -124, -478, 2328, 819
       FontFile: true
      ToUnicode: true
     Font: 
      BaseFont: HHNCYN+MSBM10
      FontSubset: true
      FirstChar: 69
      LastChar: 82
      FontDescriptor: 
       FontName: HHNCYN+MSBM10
       Flags: Symbolic
       FontBBox: -55, -420, 2343, 920
       FontFile: true
      ToUnicode: true
     Font: 
      BaseFont: LJGQWF+CharisSIL
      FontSubset: true
      FirstChar: 21
      LastChar: 252
      FontDescriptor: 
       FontName: LJGQWF+CharisSIL
       Flags: Symbolic
       FontBBox: -1418, -1092, 6144, 2600
       FontFile: true
      ToUnicode: true
     Font: 
      BaseFont: PFUYCM+t1-uni-regular
      FontSubset: true
      FirstChar: 46
      LastChar: 119
      FontDescriptor: 
       FontName: PFUYCM+t1-uni-regular
       Flags: Symbolic
       FontBBox: -168, -250, 992, 997
       FontFile: true
      ToUnicode: true
     Font: 
      BaseFont: WHHDUM+STIXMathScript-Regular
      FontSubset: true
      FirstChar: 53
      LastChar: 253
      FontDescriptor: 
       FontName: WHHDUM+STIXMathScript-Regular
       Flags: Symbolic
       FontBBox: 0, -324, 1229, 830
       FontFile: true
      ToUnicode: true
     Font: 
      BaseFont: AXUTNU+MSBM7
      FontSubset: true
      FirstChar: 78
      LastChar: 78
      FontDescriptor: 
       FontName: AXUTNU+MSBM7
       Flags: Symbolic
       FontBBox: -45, -504, 2613, 1004
       FontFile: true
      ToUnicode: true
    CIDFontType0: 
     Font: 
      BaseFont: XVZVYO+LMRoman10-Regular
      CIDSystemInfo: 
       Registry: Adobe
       Registry: Identity
       Supplement: 0
      FontDescriptor: 
       FontName: XVZVYO+LMRoman10-Regular
       Flags: Symbolic
       FontBBox: -430, -290, 1417, 1127
       FontFile3: true
    CIDFontType2: 
     Font: 
      BaseFont: XGUPJE+CharisSIL
      CIDSystemInfo: 
       Registry: Adobe
       Registry: Identity
       Supplement: 0
      FontDescriptor: 
       FontName: XGUPJE+CharisSIL
       Flags: Serif, Symbolic
       FontBBox: -692, -533, 1623, 1319
       FontFile2: true
     Font: 
      BaseFont: AAAUKD+CharisSIL
      CIDSystemInfo: 
       Registry: Adobe
       Registry: Identity
       Supplement: 0
      FontDescriptor: 
       FontName: AAAUKD+CharisSIL
       Flags: Symbolic
       FontBBox: -692, -533, 1623, 1318
       FontFile2: true
     Font: 
      BaseFont: AAAAAD+CharisSIL
      CIDSystemInfo: 
       Registry: Adobe
       Registry: Identity
       Supplement: 0
      FontDescriptor: 
       FontName: AAAAAD+CharisSIL
       Flags: Symbolic
       FontBBox: -692, -533, 1623, 1318
       FontFile2: true
     Font: 
      BaseFont: AAAALE+CharisSIL-Italic
      CIDSystemInfo: 
       Registry: Adobe
       Registry: Identity
       Supplement: 0
      FontDescriptor: 
       FontName: AAAALE+CharisSIL-Italic
       Flags: Symbolic, Italic
       FontBBox: -716, -533, 1626, 1317
       FontFile2: true
     Font: 
      BaseFont: VEVLHQ+CharisSIL-Italic
      CIDSystemInfo: 
       Registry: Adobe
       Registry: Identity
       Supplement: 0
      FontDescriptor: 
       FontName: VEVLHQ+CharisSIL-Italic
       Flags: Serif, Symbolic, Italic
       FontBBox: -716, -533, 1627, 1318
       FontFile2: true
   XMP: <x:xmpmeta xmlns:x="adobe:ns:meta/" x:xmptk="XMP Core 5.1.2">
   <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
      <rdf:Description rdf:about=""
            xmlns:ali="http://www.niso.org/schemas/ali/1.0/">
         <ali:license_ref>
            <rdf:Bag>
               <rdf:li rdf:parseType="Resource">
                  <ali:uri>http://creativecommons.org/licenses/by-nc/4.0/</ali:uri>
               </rdf:li>
            </rdf:Bag>
         </ali:license_ref>
      </rdf:Description>
      <rdf:Description rdf:about=""
            xmlns:dc="http://purl.org/dc/elements/1.1/">
         <dc:format>application/pdf</dc:format>
         <dc:identifier>10.1016/j.spl.2026.110714</dc:identifier>
         <dc:publisher>
            <rdf:Bag>
               <rdf:li>Elsevier B.V.</rdf:li>
            </rdf:Bag>
         </dc:publisher>
         <dc:description>
            <rdf:Alt>
               <rdf:li xml:lang="x-default">Statistics and Probability Letters, 235 (2026) 110714. doi:10.1016/j.spl.2026.110714</rdf:li>
            </rdf:Alt>
         </dc:description>
         <dc:subject>
            <rdf:Bag>
               <rdf:li>Brownian motion</rdf:li>
               <rdf:li>Renewal process</rdf:li>
               <rdf:li>Weak convergence</rdf:li>
               <rdf:li>Kac–Stroock approximations</rdf:li>
            </rdf:Bag>
         </dc:subject>
         <dc:title>
            <rdf:Alt>
               <rdf:li xml:lang="x-default">Kac–Stroock type approximations for the Brownian motion from renewal processes</rdf:li>
            </rdf:Alt>
         </dc:title>
         <dc:creator>
            <rdf:Seq>
               <rdf:li>Xavier Bardina</rdf:li>
               <rdf:li>Salim Boukfal</rdf:li>
            </rdf:Seq>
         </dc:creator>
      </rdf:Description>
      <rdf:Description rdf:about=""
            xmlns:jav="http://www.niso.org/schemas/jav/1.0/">
         <jav:journal_article_version>VoR</jav:journal_article_version>
      </rdf:Description>
      <rdf:Description rdf:about=""
            xmlns:pdf="http://ns.adobe.com/pdf/1.3/">
         <pdf:CreationDate--Text>16th March 2026</pdf:CreationDate--Text>
         <pdf:Producer>Acrobat Distiller 8.1.0 (Windows)</pdf:Producer>
         <pdf:Keywords>Brownian motion,Renewal process,Weak convergence,Kac–Stroock approximations</pdf:Keywords>
      </rdf:Description>
      <rdf:Description rdf:about=""
            xmlns:pdfx="http://ns.adobe.com/pdfx/1.3/">
         <pdfx:CreationDate--Text>16th March 2026</pdfx:CreationDate--Text>
         <XlEDunt-MnPmOndmGmPqQysNNntaRlt6Sz9eGnMqNm9qKmdz7nteSo9eQnMqNn9yLmduTma/>  
         <pdfx:doi>10.1016/j.spl.2026.110714</pdfx:doi>
         <pdfx:robots>noindex</pdfx:robots>
      </rdf:Description>
      <rdf:Description rdf:about=""
            xmlns:prism="http://prismstandard.org/namespaces/basic/3.0/">
         <prism:aggregationType>journal</prism:aggregationType>
         <prism:coverDate>2026-08-01</prism:coverDate>
         <prism:coverDisplayDate>1 August 2026</prism:coverDisplayDate>
         <prism:doi>10.1016/j.spl.2026.110714</prism:doi>
         <prism:issn>0167-7152</prism:issn>
         <prism:pageRange>110714</prism:pageRange>
         <prism:publicationName>Statistics and Probability Letters</prism:publicationName>
         <prism:startingPage>110714</prism:startingPage>
         <prism:url>https://doi.org/10.1016/j.spl.2026.110714</prism:url>
         <prism:volume>235</prism:volume>
      </rdf:Description>
      <rdf:Description rdf:about=""
            xmlns:tdm="http://www.w3.org/ns/tdmrep/">
         <tdm:policy>https://www.elsevier.com/tdm/tdmrep-policy.json</tdm:policy>
         <tdm:reservation>1</tdm:reservation>
      </rdf:Description>
      <rdf:Description rdf:about=""
            xmlns:xmp="http://ns.adobe.com/xap/1.0/">
         <xmp:CreateDate>2026-03-12T16:04:50</xmp:CreateDate>
         <xmp:CreatorTool>Elsevier</xmp:CreatorTool>
         <xmp:MetadataDate>2026-03-16T12:59:30</xmp:MetadataDate>
         <xmp:ModifyDate>2026-03-16T12:59:30</xmp:ModifyDate>
      </rdf:Description>
      <rdf:Description rdf:about=""
            xmlns:xmpMM="http://ns.adobe.com/xap/1.0/mm/">
         <xmpMM:DocumentID>uuid:1b499bed-4ce8-4c0c-b682-0d58baae1cbe</xmpMM:DocumentID>
         <xmpMM:InstanceID>uuid:b6ed5266-03cb-4855-90c0-636283357f42</xmpMM:InstanceID>
      </rdf:Description>
      <rdf:Description rdf:about=""
            xmlns:xmpRights="http://ns.adobe.com/xap/1.0/rights/">
         <xmpRights:Marked>True</xmpRights:Marked>
      </rdf:Description>
   </rdf:RDF>
</x:xmpmeta>
   Pages: 
    Page: 
     Label: 1
     Annotations: 
      Annotation: 
       Subtype: Link
       Contents: https://www.elsevier.com/locate/stapro
       Rect: 297, 676, 345, 682
      Annotation: 
       Subtype: Link
       Contents: https://www.elsevier.com/locate/stapro
       Rect: 251, 620, 371, 627
      Annotation: 
       Subtype: Link
       Rect: 144, 544, 152, 562
       ActionDest: 156
      Annotation: 
       Subtype: Link
       Contents: https://orcid.org/0000-0003-1803-3401
       Rect: 108, 533, 117, 542
      Annotation: 
       Subtype: Link
       Rect: 119, 536, 123, 540
       ActionDest: 156
      Annotation: 
       Subtype: Link
       Contents: https://orcid.org/0009-0007-5296-7087
       Rect: 193, 533, 202, 542
      Annotation: 
       Subtype: Link
       Rect: 128, 329, 208, 336
       ActionDest: 17
      Annotation: 
       Subtype: Link
       Rect: 214, 329, 232, 336
       ActionDest: 17
      Annotation: 
       Subtype: Link
       Rect: 177, 279, 189, 286
       ActionDest: 17
      Annotation: 
       Subtype: Link
       Rect: 196, 279, 214, 286
       ActionDest: 17
      Annotation: 
       Subtype: Link
       Rect: 137, 229, 164, 235
       ActionDest: 17
      Annotation: 
       Subtype: Link
       Rect: 170, 229, 188, 235
       ActionDest: 17
      Annotation: 
       Subtype: Link
       Rect: 477, 217, 505, 228
       ActionDest: 17
      Annotation: 
       Subtype: Link
       Rect: 39, 217, 39, 219
       ActionDest: 17
      Annotation: 
       Subtype: Link
       Rect: 62, 207, 101, 214
       ActionDest: 17
      Annotation: 
       Subtype: Link
       Rect: 107, 207, 125, 214
       ActionDest: 17
      Annotation: 
       Subtype: Link
       Rect: 431, 186, 479, 193
       ActionDest: 17
      Annotation: 
       Subtype: Link
       Rect: 485, 186, 503, 193
       ActionDest: 17
      Annotation: 
       Subtype: Link
       Rect: 62, 176, 80, 182
       ActionDest: 17
      Annotation: 
       Subtype: Link
       Contents: mailto:xavier.bardina@uab.cat
       Rect: 105, 107, 173, 116
      Annotation: 
       Subtype: Link
       Contents: mailto:salim.boukfal@uab.cat
       Rect: 215, 107, 280, 116
      Annotation: 
       Subtype: Link
       Contents: https://doi.org/10.1016/j.spl.2026.110714
       Rect: 39, 91, 177, 98
      Annotation: 
       Subtype: Link
       Rect: 188, 699, 354, 711
      Annotation: 
       Subtype: Link
       Rect: 41, 51, 197, 63
    Page: 
     Label: 2
     Annotations: 
      Annotation: 
       Subtype: Link
       Rect: 284, 672, 348, 679
       ActionDest: 17
      Annotation: 
       Subtype: Link
       Rect: 354, 672, 372, 679
       ActionDest: 17
      Annotation: 
       Subtype: Link
       Rect: 380, 672, 429, 679
       ActionDest: 17
      Annotation: 
       Subtype: Link
       Rect: 435, 672, 453, 679
       ActionDest: 17
      Annotation: 
       Subtype: Link
       Rect: 461, 672, 505, 679
       ActionDest: 17
      Annotation: 
       Subtype: Link
       Rect: 39, 672, 39, 674
       ActionDest: 17
      Annotation: 
       Subtype: Link
       Rect: 62, 662, 89, 668
       ActionDest: 17
      Annotation: 
       Subtype: Link
       Rect: 95, 662, 113, 668
       ActionDest: 17
      Annotation: 
       Subtype: Link
       Rect: 118, 662, 136, 668
       ActionDest: 17
      Annotation: 
       Subtype: Link
       Rect: 268, 639, 312, 647
       ActionDest: 17
      Annotation: 
       Subtype: Link
       Rect: 317, 639, 335, 647
       ActionDest: 17
      Annotation: 
       Subtype: Link
       Rect: 343, 639, 412, 647
       ActionDest: 17
      Annotation: 
       Subtype: Link
       Rect: 418, 639, 436, 647
       ActionDest: 17
      Annotation: 
       Subtype: Link
       Rect: 182, 576, 253, 584
       ActionDest: 17
      Annotation: 
       Subtype: Link
       Rect: 259, 576, 277, 584
       ActionDest: 17
      Annotation: 
       Subtype: Link
       Rect: 343, 544, 355, 552
       ActionDest: 17
      Annotation: 
       Subtype: Link
       Rect: 361, 544, 379, 552
       ActionDest: 17
      Annotation: 
       Subtype: Link
       Rect: 400, 544, 455, 552
       ActionDest: 17
      Annotation: 
       Subtype: Link
       Rect: 461, 544, 479, 552
       ActionDest: 17
      Annotation: 
       Subtype: Link
       Rect: 240, 293, 271, 304
       ActionDest: 1
      Annotation: 
       Subtype: Link
       Rect: 274, 293, 285, 304
       ActionDest: 1
      Annotation: 
       Subtype: Link
       Rect: 435, 293, 505, 304
       ActionDest: 17
      Annotation: 
       Subtype: Link
       Rect: 42, 282, 59, 290
       ActionDest: 17
      Annotation: 
       Subtype: Link
       Rect: 278, 239, 347, 247
       ActionDest: 17
      Annotation: 
       Subtype: Link
       Rect: 353, 239, 371, 247
       ActionDest: 17
      Annotation: 
       Subtype: Link
       Rect: 133, 130, 137, 137
       ActionDest: 1
      Annotation: 
       Subtype: Link
       Rect: 278, 119, 321, 126
       ActionDest: 17
      Annotation: 
       Subtype: Link
       Rect: 326, 119, 344, 126
       ActionDest: 17
      Annotation: 
       Subtype: Link
       Rect: 351, 119, 419, 126
       ActionDest: 17
      Annotation: 
       Subtype: Link
       Rect: 424, 119, 442, 126
       ActionDest: 17
      Annotation: 
       Subtype: Link
       Rect: 477, 98, 505, 105
       ActionDest: 17
      Annotation: 
       Subtype: Link
       Rect: 39, 98, 39, 99
       ActionDest: 17
      Annotation: 
       Subtype: Link
       Rect: 39, 87, 77, 94
       ActionDest: 17
      Annotation: 
       Subtype: Link
       Rect: 83, 87, 101, 94
       ActionDest: 17
    Page: 
     Label: 3
     Annotations: 
      Annotation: 
       Subtype: Link
       Rect: 70, 682, 104, 693
       ActionDest: 1
      Annotation: 
       Subtype: Link
       Rect: 106, 682, 118, 693
       ActionDest: 1
      Annotation: 
       Subtype: Link
       Rect: 309, 204, 346, 212
       ActionDest: 17
      Annotation: 
       Subtype: Link
       Rect: 351, 204, 369, 212
       ActionDest: 17
    Page: 
     Label: 4
     Annotations: 
      Annotation: 
       Subtype: Link
       Rect: 48, 569, 85, 576
       ActionDest: 17
      Annotation: 
       Subtype: Link
       Rect: 91, 569, 108, 576
       ActionDest: 17
      Annotation: 
       Subtype: Link
       Rect: 468, 501, 505, 508
       ActionDest: 17
      Annotation: 
       Subtype: Link
       Rect: 42, 490, 59, 498
       ActionDest: 17
      Annotation: 
       Subtype: Link
       Rect: 419, 415, 423, 424
       ActionDest: 13
      Annotation: 
       Subtype: Link
       Rect: 227, 154, 264, 163
       ActionDest: 17
      Annotation: 
       Subtype: Link
       Rect: 270, 154, 288, 163
       ActionDest: 17
    Page: 
     Label: 5
     Annotations: 
      Annotation: 
       Subtype: Link
       Contents: http://refhub.elsevier.com/S0167-7152(26)00078-7/sb1
       Rect: 39, 616, 505, 622
      Annotation: 
       Subtype: Link
       Contents: http://refhub.elsevier.com/S0167-7152(26)00078-7/sb1
       Rect: 39, 616, 39, 618
      Annotation: 
       Subtype: Link
       Contents: http://refhub.elsevier.com/S0167-7152(26)00078-7/sb1
       Rect: 50, 608, 372, 615
      Annotation: 
       Subtype: Link
       Contents: http://arxiv.org/abs/2504.08317
       Rect: 334, 599, 385, 605
      Annotation: 
       Subtype: Link
       Contents: https://arxiv.org/abs/2504.08317
       Rect: 406, 599, 503, 605
      Annotation: 
       Subtype: Link
       Contents: http://dx.doi.org/10.1515/math-2025-0234
       Rect: 366, 590, 492, 596
      Annotation: 
       Subtype: Link
       Contents: http://dx.doi.org/10.1016/S0167-7152(00)00113-9
       Rect: 118, 565, 265, 571
      Annotation: 
       Subtype: Link
       Contents: https://www.sciencedirect.com/science/article/pii/S0167715200001139
       Rect: 286, 565, 494, 571
      Annotation: 
       Subtype: Link
       Contents: http://dx.doi.org/10.1016/j.spl.2003.09.001
       Rect: 102, 548, 229, 554
      Annotation: 
       Subtype: Link
       Contents: https://www.sciencedirect.com/science/article/pii/S0167715203002578
       Rect: 250, 548, 458, 554
      Annotation: 
       Subtype: Link
       Contents: http://dx.doi.org/10.1016/j.spa.2020.04.006
       Rect: 208, 530, 337, 536
      Annotation: 
       Subtype: Link
       Contents: https://www.sciencedirect.com/science/article/pii/S0304414919304478
       Rect: 358, 530, 505, 536
      Annotation: 
       Subtype: Link
       Contents: https://www.sciencedirect.com/science/article/pii/S0304414919304478
       Rect: 39, 530, 39, 532
      Annotation: 
       Subtype: Link
       Contents: https://www.sciencedirect.com/science/article/pii/S0304414919304478
       Rect: 50, 523, 111, 528
      Annotation: 
       Subtype: Link
       Contents: http://dx.doi.org/10.1007/s00009-014-0472-4
       Rect: 50, 505, 184, 511
      Annotation: 
       Subtype: Link
       Contents: http://dx.doi.org/10.1515/math-2023-0112
       Rect: 410, 496, 505, 502
      Annotation: 
       Subtype: Link
       Contents: http://dx.doi.org/10.1515/math-2023-0112
       Rect: 39, 496, 39, 498
      Annotation: 
       Subtype: Link
       Contents: http://dx.doi.org/10.1515/math-2023-0112
       Rect: 50, 489, 81, 494
      Annotation: 
       Subtype: Link
       Contents: http://refhub.elsevier.com/S0167-7152(26)00078-7/sb9
       Rect: 39, 479, 436, 485
      Annotation: 
       Subtype: Link
       Contents: http://www.jstor.org/stable/3215716
       Rect: 395, 470, 503, 476
      Annotation: 
       Subtype: Link
       Contents: http://dx.doi.org/10.1214/aoms/1177693346
       Rect: 87, 453, 218, 459
      Annotation: 
       Subtype: Link
       Contents: http://dx.doi.org/10.1216/RMJ-1974-4-3-497
       Rect: 372, 445, 503, 451
      Annotation: 
       Subtype: Link
       Contents: http://dx.doi.org/10.1016/0378-4371(89)90071-X
       Rect: 453, 436, 505, 442
      Annotation: 
       Subtype: Link
       Contents: http://dx.doi.org/10.1016/0378-4371(89)90071-X
       Rect: 39, 436, 39, 438
      Annotation: 
       Subtype: Link
       Contents: http://dx.doi.org/10.1016/0378-4371(89)90071-X
       Rect: 50, 428, 144, 434
      Annotation: 
       Subtype: Link
       Contents: https://www.sciencedirect.com/science/article/pii/037843718990071X
       Rect: 165, 428, 370, 434
      Annotation: 
       Subtype: Link
       Contents: http://refhub.elsevier.com/S0167-7152(26)00078-7/sb14
       Rect: 39, 419, 376, 425
  Checksum: 481c1867
   Type: CRC32
  Checksum: d430106851cd0bdd52d171fc2a1ae4e3
   Type: MD5
  Checksum: 042ef056124dee7b5c65be9f1408575436bb5072
   Type: SHA-1
  Checksum: decbd5ee7ea957493a8cf2ae8feb73304cd208aa5ad9cc1c80667d9cbc3d207d
   Type: SHA-256