On the complete convergence for uncertain random variables
Abstract In some complex systems, the randomness and uncertainty phenomena may arise simultaneously, which inspires us to develop the uncertain random variable in chance space. Based on the chance theory, we propose the concept of complete convergence and investigate the relations among the existing...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Yu, Yuncai [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2022 |
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| Schlagwörter: |
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| Anmerkung: |
© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021 |
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| Übergeordnetes Werk: |
Enthalten in: Soft Computing - Springer-Verlag, 2003, 26(2022), 3 vom: 15. Jan., Seite 1025-1031 |
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| Übergeordnetes Werk: |
volume:26 ; year:2022 ; number:3 ; day:15 ; month:01 ; pages:1025-1031 |
| Links: |
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| DOI / URN: |
10.1007/s00500-021-06504-8 |
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SPR046045775 |
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10.1007/s00500-021-06504-8 doi (DE-627)SPR046045775 (SPR)s00500-021-06504-8-e DE-627 ger DE-627 rakwb eng Yu, Yuncai verfasserin aut On the complete convergence for uncertain random variables 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021 Abstract In some complex systems, the randomness and uncertainty phenomena may arise simultaneously, which inspires us to develop the uncertain random variable in chance space. Based on the chance theory, we propose the concept of complete convergence and investigate the relations among the existing common types of convergence including convergence almost surely, convergence in measure, convergence in distribution and convergence in mean. All of the relations are illustrated via the corresponding examples or counterexamples. Additionally, we give an equivalent condition and a sufficient condition of convergence completely for uncertain random variables and provide an example to explain the conditions. Complete convergence (dpeaa)DE-He213 Chance theory (dpeaa)DE-He213 Uncertain random variable (dpeaa)DE-He213 Equivalent condition (dpeaa)DE-He213 Sufficient condition (dpeaa)DE-He213 Liu, Xinsheng (orcid)0000-0002-3348-9493 aut Zhang, Yu aut Jia, Zhifu aut Enthalten in Soft Computing Springer-Verlag, 2003 26(2022), 3 vom: 15. Jan., Seite 1025-1031 (DE-627)SPR006469531 nnns volume:26 year:2022 number:3 day:15 month:01 pages:1025-1031 https://dx.doi.org/10.1007/s00500-021-06504-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 26 2022 3 15 01 1025-1031 |
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10.1007/s00500-021-06504-8 doi (DE-627)SPR046045775 (SPR)s00500-021-06504-8-e DE-627 ger DE-627 rakwb eng Yu, Yuncai verfasserin aut On the complete convergence for uncertain random variables 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021 Abstract In some complex systems, the randomness and uncertainty phenomena may arise simultaneously, which inspires us to develop the uncertain random variable in chance space. Based on the chance theory, we propose the concept of complete convergence and investigate the relations among the existing common types of convergence including convergence almost surely, convergence in measure, convergence in distribution and convergence in mean. All of the relations are illustrated via the corresponding examples or counterexamples. Additionally, we give an equivalent condition and a sufficient condition of convergence completely for uncertain random variables and provide an example to explain the conditions. Complete convergence (dpeaa)DE-He213 Chance theory (dpeaa)DE-He213 Uncertain random variable (dpeaa)DE-He213 Equivalent condition (dpeaa)DE-He213 Sufficient condition (dpeaa)DE-He213 Liu, Xinsheng (orcid)0000-0002-3348-9493 aut Zhang, Yu aut Jia, Zhifu aut Enthalten in Soft Computing Springer-Verlag, 2003 26(2022), 3 vom: 15. Jan., Seite 1025-1031 (DE-627)SPR006469531 nnns volume:26 year:2022 number:3 day:15 month:01 pages:1025-1031 https://dx.doi.org/10.1007/s00500-021-06504-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 26 2022 3 15 01 1025-1031 |
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Abstract In some complex systems, the randomness and uncertainty phenomena may arise simultaneously, which inspires us to develop the uncertain random variable in chance space. Based on the chance theory, we propose the concept of complete convergence and investigate the relations among the existing common types of convergence including convergence almost surely, convergence in measure, convergence in distribution and convergence in mean. All of the relations are illustrated via the corresponding examples or counterexamples. Additionally, we give an equivalent condition and a sufficient condition of convergence completely for uncertain random variables and provide an example to explain the conditions. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021 |
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Abstract In some complex systems, the randomness and uncertainty phenomena may arise simultaneously, which inspires us to develop the uncertain random variable in chance space. Based on the chance theory, we propose the concept of complete convergence and investigate the relations among the existing common types of convergence including convergence almost surely, convergence in measure, convergence in distribution and convergence in mean. All of the relations are illustrated via the corresponding examples or counterexamples. Additionally, we give an equivalent condition and a sufficient condition of convergence completely for uncertain random variables and provide an example to explain the conditions. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021 |
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Abstract In some complex systems, the randomness and uncertainty phenomena may arise simultaneously, which inspires us to develop the uncertain random variable in chance space. Based on the chance theory, we propose the concept of complete convergence and investigate the relations among the existing common types of convergence including convergence almost surely, convergence in measure, convergence in distribution and convergence in mean. All of the relations are illustrated via the corresponding examples or counterexamples. Additionally, we give an equivalent condition and a sufficient condition of convergence completely for uncertain random variables and provide an example to explain the conditions. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021 |
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Based on the chance theory, we propose the concept of complete convergence and investigate the relations among the existing common types of convergence including convergence almost surely, convergence in measure, convergence in distribution and convergence in mean. All of the relations are illustrated via the corresponding examples or counterexamples. Additionally, we give an equivalent condition and a sufficient condition of convergence completely for uncertain random variables and provide an example to explain the conditions.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Complete convergence</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Chance theory</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Uncertain random variable</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Equivalent condition</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Sufficient condition</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Liu, Xinsheng</subfield><subfield code="0">(orcid)0000-0002-3348-9493</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Zhang, Yu</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Jia, Zhifu</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Soft Computing</subfield><subfield code="d">Springer-Verlag, 2003</subfield><subfield code="g">26(2022), 3 vom: 15. Jan., Seite 1025-1031</subfield><subfield code="w">(DE-627)SPR006469531</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:26</subfield><subfield code="g">year:2022</subfield><subfield code="g">number:3</subfield><subfield code="g">day:15</subfield><subfield code="g">month:01</subfield><subfield code="g">pages:1025-1031</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://dx.doi.org/10.1007/s00500-021-06504-8</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_SPRINGER</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">26</subfield><subfield code="j">2022</subfield><subfield code="e">3</subfield><subfield code="b">15</subfield><subfield code="c">01</subfield><subfield code="h">1025-1031</subfield></datafield></record></collection>
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