Mathematica Pannonica
Volume/Issue:
Volume 29_NS3: Issue 1
On the Complete Convergence of Martingale
Authors:
Mengmeng Chang College of Mathematics and Information Science, Henan Normal University, Henan Province, 453007, China
College of Mathematics and Information Science, Anyang Institute of Technology, Henan Province, 455000, China

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Yu Miao College of Mathematics and Information Science, Henan Normal University, Henan Province, 453007, China
Henan Engineering Laboratory for Big Data Statistical Analysis and Optimal Control, Henan Normal University, Henan Province, 453007, China

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Pages:
111–119
Online Publication Date:
11 May 2023
Publication Date:
19 May 2023
Article Category:
Research Article
DOI:
https://doi.org/10.1556/314.2023.00010
Keywords (English):
Martingale; complete convergence
Open access

In the present paper, we establish the convergence rates of the single logarithm and the iterated logarithm for martingale differences which give some further results for the open question in Stoica [6].

  • [1]

    Chen, Y. X., Zhang, S. L., and Ma, F. Q. On the complete convergence for martingale difference sequence. Comm. Statist. Theory Methods 46 (15) (2017), 7603–7611.

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  • [2]

    Davis, J. A. Convergence rates for the law of the iterated logarithm. Ann. Math. Statist. 39 (1968), 1479–1485.

  • [3]

    Davis, J. A. Convergence rates for probabilities of moderate deviations. Ann. Math. Statist. 39 (1968), 2016–2028.

  • [4]

    Miao, Y., Yang, G. Y. and Stoica, G. On the rate of convergence in the strong law of large numbers for martingales. Stochastics 87 (2) (2015), 185–198.

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  • [5]

    Stoica, G. Davis-type theorems for martingale difference sequences. J. Appl. Math. Stoch. Anal. 2005, no. 2, 159–165.

  • [6]

    Stoica, G. Series of moderate deviation probabilities for martingales. J. Math. Anal. Appl. 308 (2) (2005), 759–763.

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Cover Mathematica Pannonica
Mathematica Pannonica
Print ISSN:
0865-2090
Online ISSN:
2786-0752
The Instruction for Authors is available in PDF format. Please, download the file from HERE.
Please, download the LaTeX template from HERE.

Editor in Chief: László TÓTH (University of Pécs)

Honorary Editors in Chief:

  • † István GYŐRI (University of Pannonia, Veszprém)
  • János PINTZ (Rényi Institute of Mathematics)
  • Ferenc SCHIPP (Eötvös University Budapest and University of Pécs)
  • Sándor SZABÓ (University of Pécs)
     

Deputy Editors in Chief:

  • Erhard AICHINGER (JKU Linz)
  • Ferenc HARTUNG (University of Pannonia, Veszprém)
  • Ferenc WEISZ (Eötvös University, Budapest)

Editorial Board

  • Attila BÉRCZES (University of Debrecen)
  • István BERKES (Rényi Institute of Mathematics)
  • Károly BEZDEK (University of Calgary)
  • György DÓSA (University of Pannonia, Veszprém)
  • Balázs KIRÁLY – Managing Editor (University of Pécs)
  • Vedran KRCADINAC (University of Zagreb) 
  • Željka MILIN ŠIPUŠ (University of Zagreb)
  • Gábor NYUL (University of Debrecen)
  • Margit PAP (University of Pécs)
  • István PINK (University of Debrecen)
  • Mihály PITUK (University of Pannonia, Veszprém)
  • Jörg THUSWALDNER (Montanuniversität Leoben)
  • Zsolt TUZA (University of Pannonia, Veszprém)

Advisory Board

  • Szilárd RÉVÉSZ (Rényi Institute of Mathematics)  - Chair
  • Gabriella BÖHM
  • György GÁT (University of Debrecen)

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Mathematica Pannonica
Language English
Size A4
Year of
Foundation		 1990
Volumes
per Year		 1
Issues
per Year		 2
Founder Akadémiai Kiadó
Founder's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Publisher Akadémiai Kiadó
Publisher's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Responsible
Publisher		 Chief Executive Officer, Akadémiai Kiadó
ISSN 2786-0752 (Online)
ISSN 0865-2090 (Print)

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