d0d46f7d6378a6ac42b3d11d686d3dfa OpeMat_a2026_m3_v24_n1.pdf 24718fab699bfb4f15b4d841159f16981d9fe172 OpeMat_a2026_m3_v24_n1.pdf 00b72533365494124b4adcda36f89dc8f42eb874c7120162fe28ae6d47d0a2ba OpeMat_a2026_m3_v24_n1.pdf Title: On the weak convergence of multiparameter stochastic integrals Subject: Author: Xavier Bardina Creator: LaTeX with hyperref package + hypdvips Producer: Acrobat Distiller 8.0.0 (Windows) CreationDate: Thu Mar 19 13:28:43 2026 CET ModDate: Thu Mar 19 13:31:52 2026 CET Custom Metadata: no Metadata Stream: yes Tagged: no UserProperties: no Suspects: no Form: none JavaScript: no Pages: 21 Encrypted: no Page size: 595.276 x 793.701 pts Page rot: 0 File size: 696689 bytes Optimized: yes PDF version: 1.7 name type encoding emb sub uni object ID ------------------------------------ ----------------- ---------------- --- --- --- --------- De-Gruyter-Sans-Regular Type 1C WinAnsi yes no no 567 0 De-Gruyter-Sans-Bold Type 1C WinAnsi yes no no 569 0 De-Gruyter-Serif-Bold Type 1C MacRoman yes no no 571 0 De-Gruyter-Serif-Regular Type 1C Custom yes no yes 576 0 STIXMathCalligraphy-Regular Type 1C Custom yes no yes 581 0 STIXMath-Italic Type 1C Custom yes no yes 586 0 De-Gruyter-Serif-Italic Type 1C MacRoman yes no no 588 0 STIXMath-Regular Type 1C Custom yes no yes 593 0 STIXMathBlackboard-Regular Type 1C Custom yes no yes 599 0 STIXMathExtensions-Regular Type 1C Custom yes no yes 605 0 STIXMathScript-Regular Type 1C Custom yes no yes 252 0 LEBNLC+rsfs7 Type 1C WinAnsi yes yes no 249 0 STIXMathSans-Regular Type 1C Custom yes no yes 262 0 De-Gruyter-Sans-Italic Type 1C WinAnsi yes no no 298 0 Jhove (Rel. 1.28.0, 2023-05-18) Date: 2026-05-22 04:09:57 CEST RepresentationInformation: OpeMat_a2026_m3_v24_n1.pdf ReportingModule: PDF-hul, Rel. 1.12.4 (2023-03-16) LastModified: 2026-05-21 12:32:43 CEST Size: 696689 Format: PDF Version: 1.7 Status: Well-Formed, but not valid SignatureMatches: PDF-hul ErrorMessage: Invalid indirect destination - referenced object 'j_math-2025-0234_aff_001' cannot be found ID: PDF-HUL-149 ErrorMessage: edu.harvard.hul.ois.jhove.module.pdf.PdfInvalidException: Invalid indirect destination - referenced object 'j_math-2025-0234_aff_001' cannot be found ID: PDF-HUL-122 Offset: 666628 MIMEtype: application/pdf Profile: Linearized PDF PDFMetadata: Objects: 647 FreeObjects: 1 IncrementalUpdates: 1 DocumentCatalog: PageLayout: SinglePage PageMode: UseOutlines Language: en Outlines: Item: Title: 1 Introduction Destination: section.1 Item: Title: 2 Preliminaries Destination: section.2 Item: Title: 3 Statement and proof of the main result Destination: section.3 Children: Item: Title: 3.1 Convergence for the Donsker kernels Destination: subsection.3.1 Item: Title: 3.2 Convergence for the Kac-Stroock kernels Destination: subsection.3.2 Item: Title: A Appendix Destination: section*.2 Info: Title: On the weak convergence of multiparameter stochastic integrals Author: Xavier Bardina Subject: Creator: LaTeX with hyperref package + hypdvips Producer: Acrobat Distiller 8.0.0 (Windows) CreationDate: Thu Mar 19 13:58:43 CET 2026 ModDate: Thu Mar 19 14:01:52 CET 2026 ID: 0xae70f7ef0a7b47b8cc20a550e6fb257a, 0x1ed711914a82e9459d51e1a15bc31f04 Filters: FilterPipeline: FlateDecode Fonts: Type1: Font: BaseFont: De-Gruyter-Serif-Regular FirstChar: 0 LastChar: 255 FontDescriptor: FontName: De-Gruyter-Serif-Regular Flags: Serif, Symbolic FontBBox: 0, -227, 873, 736 FontFile3: true EncodingDictionary: Differences: true ToUnicode: true Font: BaseFont: STIXMathCalligraphy-Regular FirstChar: 0 LastChar: 255 FontDescriptor: FontName: STIXMathCalligraphy-Regular Flags: Symbolic FontBBox: 31, -320, 639, 824 FontFile3: true EncodingDictionary: Differences: true ToUnicode: true Font: BaseFont: STIXMathSans-Regular FirstChar: 0 LastChar: 255 FontDescriptor: FontName: STIXMathSans-Regular Flags: Symbolic FontBBox: -124, -232, 1151, 819 FontFile3: true EncodingDictionary: Differences: true ToUnicode: true Font: BaseFont: STIXMath-Italic FirstChar: 0 LastChar: 255 FontDescriptor: FontName: STIXMath-Italic Flags: Symbolic, Italic FontBBox: 39, -183, 621, 668 FontFile3: true EncodingDictionary: Differences: true ToUnicode: true Font: BaseFont: De-Gruyter-Sans-Italic FirstChar: 0 LastChar: 233 FontDescriptor: FontName: De-Gruyter-Sans-Italic Flags: Nonsymbolic, Italic FontBBox: -30, -228, 664, 722 FontFile3: true Encoding: WinAnsiEncoding Font: BaseFont: De-Gruyter-Serif-Italic FirstChar: 0 LastChar: 240 FontDescriptor: FontName: De-Gruyter-Serif-Italic Flags: Serif, Nonsymbolic, Italic FontBBox: -126, -228, 1005, 732 FontFile3: true Encoding: MacRomanEncoding Font: BaseFont: STIXMath-Regular FirstChar: 0 LastChar: 255 FontDescriptor: FontName: STIXMath-Regular Flags: Symbolic FontBBox: -970, -341, 1096, 1023 FontFile3: true EncodingDictionary: Differences: true ToUnicode: true Font: BaseFont: STIXMathBlackboard-Regular FirstChar: 0 LastChar: 255 FontDescriptor: FontName: STIXMathBlackboard-Regular Flags: Symbolic FontBBox: -15, -424, 1388, 930 FontFile3: true EncodingDictionary: Differences: true ToUnicode: true Font: BaseFont: De-Gruyter-Sans-Regular FirstChar: 0 LastChar: 242 FontDescriptor: FontName: De-Gruyter-Sans-Regular Flags: Nonsymbolic FontBBox: 0, -228, 730, 722 FontFile3: true Encoding: WinAnsiEncoding Font: BaseFont: De-Gruyter-Sans-Bold FirstChar: 0 LastChar: 173 FontDescriptor: FontName: De-Gruyter-Sans-Bold Flags: Nonsymbolic, ForceBold FontBBox: 0, -228, 745, 727 FontFile3: true Encoding: WinAnsiEncoding Font: BaseFont: LEBNLC+rsfs7 FontSubset: true FirstChar: 70 LastChar: 70 FontDescriptor: FontName: LEBNLC+rsfs7 Flags: Nonsymbolic, Italic FontBBox: 15, -302, 1349, 728 FontFile3: true Encoding: WinAnsiEncoding Font: BaseFont: De-Gruyter-Serif-Bold FirstChar: 0 LastChar: 240 FontDescriptor: FontName: De-Gruyter-Serif-Bold Flags: Serif, Nonsymbolic, ForceBold FontBBox: 0, -227, 571, 730 FontFile3: true Encoding: MacRomanEncoding Font: BaseFont: STIXMathScript-Regular FirstChar: 0 LastChar: 255 FontDescriptor: FontName: STIXMathScript-Regular Flags: Symbolic FontBBox: 0, -324, 1229, 830 FontFile3: true EncodingDictionary: Differences: true ToUnicode: true Font: BaseFont: STIXMathExtensions-Regular FirstChar: 0 LastChar: 255 FontDescriptor: FontName: STIXMathExtensions-Regular Flags: Symbolic FontBBox: 39, -1384, 1202, 959 FontFile3: true EncodingDictionary: Differences: true ToUnicode: true XMP: 2026-03-19T18:01:52+05:30 2026-03-19T17:58:43+05:30 2026-03-19T18:01:52+05:30 LaTeX with hyperref package + hypdvips application/pdf On the weak convergence of multiparameter stochastic integrals 2026 the author(s), published by De Gruyter, Berlin/Boston Xavier Bardina Brownian sheet random walk Poisson process Kac-Stroock kernels Donsker kernels journal Open Mathematics 2026 the author(s), published by De Gruyter, Berlin/Boston 1-21 1 21 10.1515/math-2025-0234 https://doi.org/10.1515/math-2025-0234 10.1515/math-2025-0234 https://doi.org/10.1515/math-2025-0234 True https://www.degruyter.com/page/terms-conditions?language=en Print Acrobat Distiller 8.0.0 (Windows) uuid:7cbe53a4-ba2d-4c98-afe6-e434169d008b uuid:e657cd33-6a9c-4d65-bcbc-53e6af03ec6c De Gruyter XMP Schema for WEB PDF http://www.degruyter.com/ns//web-pdf/ dg 10.1515/math-2025-0234 Text external The Digital Object Identifier of document https://doi.org/10.1515/math-2025-0234 text external The corresponding URL of the Digital Object Identifier. Pages: Page: Label: 1 Annotations: Annotation: Subtype: Link Rect: 120, 685, 122, 687 Destination: null Annotation: Subtype: Link Rect: 215, 685, 217, 687 Destination: null Annotation: Subtype: Link Rect: 50, 605, 180, 615 Annotation: Subtype: Link Rect: 163, 365, 175, 375 Destination: 234 Annotation: Subtype: Link Rect: 186, 365, 199, 375 Destination: 234 Annotation: Subtype: Link Rect: 164, 313, 182, 323 Destination: 1 Annotation: Subtype: Link Rect: 95, 128, 173, 136 Annotation: Subtype: Link Rect: 175, 126, 302, 136 Annotation: Subtype: Link Rect: 73, 106, 148, 114 Annotation: Subtype: Link Rect: 150, 105, 277, 114 Thumb: true Page: Label: 2 Annotations: Annotation: Subtype: Link Rect: 457, 651, 470, 661 Destination: 234 Annotation: Subtype: Link Rect: 489, 651, 502, 661 Destination: 234 Annotation: Subtype: Link Rect: 529, 599, 541, 609 Destination: 234 Annotation: Subtype: Link Rect: 315, 496, 352, 505 Destination: 1 Annotation: Subtype: Link Rect: 195, 483, 233, 492 Destination: 44 Annotation: Subtype: Link Rect: 411, 483, 471, 492 Destination: 85 Annotation: Subtype: Link Rect: 490, 483, 502, 492 Destination: 127 Thumb: true Page: Label: 3 Annotations: Annotation: Subtype: Link Rect: 209, 416, 220, 426 Destination: 234 Annotation: Subtype: Link Rect: 131, 389, 171, 400 Destination: 212 Annotation: Subtype: Link Rect: 315, 390, 333, 400 Destination: 17 Thumb: true Page: Label: 4 Annotations: Annotation: Subtype: Link Rect: 183, 597, 189, 606 Destination: 234 Annotation: Subtype: Link Rect: 170, 468, 182, 478 Destination: 234 Annotation: Subtype: Link Rect: 297, 416, 309, 426 Destination: 234 Annotation: Subtype: Link Rect: 326, 416, 339, 426 Destination: 234 Annotation: Subtype: Link Rect: 206, 206, 257, 215 Destination: 28 Annotation: Subtype: Link Rect: 128, 192, 141, 202 Destination: 234 Annotation: Subtype: Link Rect: 344, 193, 389, 202 Destination: 44 Thumb: true Page: Label: 5 Annotations: Annotation: Subtype: Link Rect: 123, 451, 130, 459 Destination: 234 Annotation: Subtype: Link Rect: 192, 143, 211, 153 Destination: 44 Thumb: true Page: Label: 6 Annotations: Annotation: Subtype: Link Rect: 490, 684, 508, 695 Destination: 28 Annotation: Subtype: Link Rect: 205, 672, 223, 682 Destination: 28 Annotation: Subtype: Link Rect: 403, 673, 453, 682 Destination: 54 Annotation: Subtype: Link Rect: 436, 564, 455, 574 Destination: 28 Annotation: Subtype: Link Rect: 323, 551, 341, 561 Destination: 28 Annotation: Subtype: Link Rect: 322, 473, 340, 483 Destination: 54 Annotation: Subtype: Link Rect: 389, 447, 407, 457 Destination: 54 Annotation: Subtype: Link Rect: 172, 409, 223, 418 Destination: 54 Annotation: Subtype: Link Rect: 325, 383, 373, 392 Destination: 85 Annotation: Subtype: Link Rect: 392, 383, 404, 392 Destination: 127 Annotation: Subtype: Link Rect: 405, 369, 423, 379 Destination: 54 Annotation: Subtype: Link Rect: 319, 279, 337, 289 Destination: 54 Thumb: true Page: Label: 7 Annotations: Annotation: Subtype: Link Rect: 216, 581, 267, 590 Destination: 28 Thumb: true Page: Label: 8 Annotations: Annotation: Subtype: Link Rect: 119, 684, 137, 694 Destination: 54 Annotation: Subtype: Link Rect: 525, 590, 543, 600 Destination: 44 Annotation: Subtype: Link Rect: 245, 484, 290, 492 Destination: 44 Annotation: Subtype: Link Rect: 385, 224, 403, 234 Destination: 54 Annotation: Subtype: Link Rect: 187, 210, 248, 221 Destination: 85 Annotation: Subtype: Link Rect: 356, 186, 374, 196 Destination: 17 Thumb: true Page: Label: 9 Thumb: true Page: Label: 10 Thumb: true Page: Label: 11 Annotations: Annotation: Subtype: Link Rect: 250, 303, 268, 313 Destination: 108 Thumb: true Page: Label: 12 Annotations: Annotation: Subtype: Link Rect: 224, 592, 242, 602 Destination: 54 Annotation: Subtype: Link Rect: 370, 523, 388, 533 Destination: 54 Annotation: Subtype: Link Rect: 171, 511, 208, 520 Destination: 44 Annotation: Subtype: Link Rect: 483, 484, 501, 494 Destination: 54 Annotation: Subtype: Link Rect: 454, 472, 499, 481 Destination: 127 Annotation: Subtype: Link Rect: 399, 458, 411, 468 Destination: 234 Annotation: Subtype: Link Rect: 102, 330, 120, 340 Destination: 127 Annotation: Subtype: Link Rect: 220, 183, 238, 193 Destination: 127 Thumb: true Page: Label: 13 Annotations: Annotation: Subtype: Link Rect: 300, 136, 319, 146 Destination: 144 Annotation: Subtype: Link Rect: 191, 96, 236, 105 Destination: 127 Thumb: true Page: Label: 14 Annotations: Annotation: Subtype: Link Rect: 286, 714, 305, 724 Destination: 127 Annotation: Subtype: Link Rect: 217, 688, 236, 698 Destination: 127 Annotation: Subtype: Link Rect: 523, 455, 541, 465 Destination: 28 Annotation: Subtype: Link Rect: 273, 224, 285, 234 Destination: 234 Annotation: Subtype: Link Rect: 333, 139, 351, 149 Destination: 155 Thumb: true Page: Label: 15 Annotations: Annotation: Subtype: Link Rect: 100, 621, 118, 631 Destination: 155 Annotation: Subtype: Link Rect: 61, 127, 80, 137 Destination: 169 Thumb: true Page: Label: 16 Thumb: true Page: Label: 17 Annotations: Annotation: Subtype: Link Rect: 315, 465, 360, 474 Destination: 127 Annotation: Subtype: Link Rect: 284, 426, 329, 435 Destination: 127 Annotation: Subtype: Link Rect: 89, 399, 107, 409 Destination: 54 Annotation: Subtype: Link Rect: 213, 360, 231, 370 Destination: 54 Thumb: true Page: Label: 18 Annotations: Annotation: Subtype: Link Rect: 204, 714, 222, 724 Destination: 189 Thumb: true Page: Label: 19 Annotations: Annotation: Subtype: Link Rect: 423, 585, 441, 595 Destination: 17 Annotation: Subtype: Link Rect: 346, 520, 364, 530 Destination: 17 Annotation: Subtype: Link Rect: 182, 481, 239, 491 Destination: 54 Thumb: true Page: Label: 20 Annotations: Annotation: Subtype: Link Rect: 261, 92, 277, 102 Destination: 234 Thumb: true Page: Label: 21 Thumb: true Checksum: 863ac06c Type: CRC32 Checksum: d0d46f7d6378a6ac42b3d11d686d3dfa Type: MD5 Checksum: 24718fab699bfb4f15b4d841159f16981d9fe172 Type: SHA-1 Checksum: 00b72533365494124b4adcda36f89dc8f42eb874c7120162fe28ae6d47d0a2ba Type: SHA-256