Limit Theorems of Integrals with Respect to Vector Random Measures in Complete Paranormed Spaces

Renying Zeng

doi:doi:10.11648/j.ijsd.20170304.14

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Limit Theorems of Integrals with Respect to Vector Random Measures in Complete Paranormed Spaces

Renying Zeng

Published in International Journal of Statistical Distributions and Applications (Volume 3, Issue 4)

Received: 7 September 2017 Accepted: 26 September 2017 Published: 15 November 2017

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Abstract

This paper studies random integral of the form, where f is a function taking value in a paranormed vector space X, and M is an independent scattered vector random measure. Random integrals of this type are a natural generalization of random series with paranormed space valued coefficients. Some limit theorems of integrals with respect to vector random measures are proved.

Published in	International Journal of Statistical Distributions and Applications (Volume 3, Issue 4)
DOI	10.11648/j.ijsd.20170304.14
Page(s)	81-86
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Paranormed Vector Space, Random Measure, Random Integral, Limit Theorem, Convergence in Probability

References

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APA Style

Renying Zeng. (2017). Limit Theorems of Integrals with Respect to Vector Random Measures in Complete Paranormed Spaces. International Journal of Statistical Distributions and Applications, 3(4), 81-86. https://doi.org/10.11648/j.ijsd.20170304.14

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ACS Style

Renying Zeng. Limit Theorems of Integrals with Respect to Vector Random Measures in Complete Paranormed Spaces. Int. J. Stat. Distrib. Appl. 2017, 3(4), 81-86. doi: 10.11648/j.ijsd.20170304.14

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AMA Style

Renying Zeng. Limit Theorems of Integrals with Respect to Vector Random Measures in Complete Paranormed Spaces. Int J Stat Distrib Appl. 2017;3(4):81-86. doi: 10.11648/j.ijsd.20170304.14

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@article{10.11648/j.ijsd.20170304.14,
  author = {Renying Zeng},
  title = {Limit Theorems of Integrals with Respect to Vector Random Measures in Complete Paranormed Spaces},
  journal = {International Journal of Statistical Distributions and Applications},
  volume = {3},
  number = {4},
  pages = {81-86},
  doi = {10.11648/j.ijsd.20170304.14},
  url = {https://doi.org/10.11648/j.ijsd.20170304.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsd.20170304.14},
  abstract = {This paper studies random integral of the form, where f is a function taking value in a paranormed vector space X, and M is an independent scattered vector random measure. Random integrals of this type are a natural generalization of random series with paranormed space valued coefficients. Some limit theorems of integrals with respect to vector random measures are proved.},
 year = {2017}
}

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TY  - JOUR
T1  - Limit Theorems of Integrals with Respect to Vector Random Measures in Complete Paranormed Spaces
AU  - Renying Zeng
Y1  - 2017/11/15
PY  - 2017
N1  - https://doi.org/10.11648/j.ijsd.20170304.14
DO  - 10.11648/j.ijsd.20170304.14
T2  - International Journal of Statistical Distributions and Applications
JF  - International Journal of Statistical Distributions and Applications
JO  - International Journal of Statistical Distributions and Applications
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EP  - 86
PB  - Science Publishing Group
SN  - 2472-3509
UR  - https://doi.org/10.11648/j.ijsd.20170304.14
AB  - This paper studies random integral of the form, where f is a function taking value in a paranormed vector space X, and M is an independent scattered vector random measure. Random integrals of this type are a natural generalization of random series with paranormed space valued coefficients. Some limit theorems of integrals with respect to vector random measures are proved.
VL  - 3
IS  - 4
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Author Information

Renying Zeng

School of Mathematical Sciences, Chongqing Normal University, Chongqing, China

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Plain Text BibTeX RIS

APA Style

Renying Zeng. (2017). Limit Theorems of Integrals with Respect to Vector Random Measures in Complete Paranormed Spaces. International Journal of Statistical Distributions and Applications, 3(4), 81-86. https://doi.org/10.11648/j.ijsd.20170304.14

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ACS Style

Renying Zeng. Limit Theorems of Integrals with Respect to Vector Random Measures in Complete Paranormed Spaces. Int. J. Stat. Distrib. Appl. 2017, 3(4), 81-86. doi: 10.11648/j.ijsd.20170304.14

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AMA Style

Renying Zeng. Limit Theorems of Integrals with Respect to Vector Random Measures in Complete Paranormed Spaces. Int J Stat Distrib Appl. 2017;3(4):81-86. doi: 10.11648/j.ijsd.20170304.14

Copy | Download

@article{10.11648/j.ijsd.20170304.14,
  author = {Renying Zeng},
  title = {Limit Theorems of Integrals with Respect to Vector Random Measures in Complete Paranormed Spaces},
  journal = {International Journal of Statistical Distributions and Applications},
  volume = {3},
  number = {4},
  pages = {81-86},
  doi = {10.11648/j.ijsd.20170304.14},
  url = {https://doi.org/10.11648/j.ijsd.20170304.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsd.20170304.14},
  abstract = {This paper studies random integral of the form, where f is a function taking value in a paranormed vector space X, and M is an independent scattered vector random measure. Random integrals of this type are a natural generalization of random series with paranormed space valued coefficients. Some limit theorems of integrals with respect to vector random measures are proved.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Limit Theorems of Integrals with Respect to Vector Random Measures in Complete Paranormed Spaces
AU  - Renying Zeng
Y1  - 2017/11/15
PY  - 2017
N1  - https://doi.org/10.11648/j.ijsd.20170304.14
DO  - 10.11648/j.ijsd.20170304.14
T2  - International Journal of Statistical Distributions and Applications
JF  - International Journal of Statistical Distributions and Applications
JO  - International Journal of Statistical Distributions and Applications
SP  - 81
EP  - 86
PB  - Science Publishing Group
SN  - 2472-3509
UR  - https://doi.org/10.11648/j.ijsd.20170304.14
AB  - This paper studies random integral of the form, where f is a function taking value in a paranormed vector space X, and M is an independent scattered vector random measure. Random integrals of this type are a natural generalization of random series with paranormed space valued coefficients. Some limit theorems of integrals with respect to vector random measures are proved.
VL  - 3
IS  - 4
ER  -

Copy | Download