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

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), 2017. Published by Science Publishing Group

Keywords

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

References
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[6] L. Egghe, The Radon-Nikodym Property, densibility and Martingles in Loccally Convex Space, Pacific Journal of Mathematics, 87(1980)2, 313-322.
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[10] N. Guillotin-Plantard and V. Ladret, Limit Theorems for U-statistics Indexed by a One Dimensional Random Walk, ESAIM: Probability and Statistics, 9(2005), 98-115.
[11] H. Tsukahara, On the Convergence of Measurable Processes and Prediction Processes, Illinois Journal of Mathematics, 51(2007)4, 1231–1242.
[12] X. F. Yang, Integral Convergence Related to Weak Convergence of Measures, Applied Mathematical Sciences, 56(2011)5, 2775 – 2779.
[13] T. Grbic and S. Medic, Weak Convergence of Sequences of Distorted Probabilities, SISY 2015, Proceedings of IEEE 13th International Symposium on Intelligent System and Informatics, Sept. 2015, 307-318, Subotica, Serbia.
[14] T. E. Govindan, Weak Convergence of Probability Measures of Yosida Approximate Mild Solutions of McKean-Vlasov Type Stochastic Evolution Equations, Seventh International Conference on Dynamic Systems and Applications & Fifth International Conference on Neural, Parallel, and Scientific Computations, May 2015, Atlanta, USA.
[15] P. Puchala, Weak Convergence in L1 of the Sequences of Monotonic Functions, Journal of Applied Mathematics and Computational Mechanics 13(2014)3, 195-199.
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[18] W. Lohrl and T. Ripple, Boundedly Finite Measures: Separation and Convergence by an Algebra of Functions, Electronic Communication of Probability, 21(2016)60, 1–16.
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Cite This Article
  • 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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    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.
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Author Information
  • School of Mathematical Sciences, Chongqing Normal University, Chongqing, China

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