Title

STATISTICAL CONVERGENCE OF
ASYMPTOTIC MARTINGALES

Authors

Danjela Braho, Edlira Donefski
Department of Mathematics, Informatics and Physics
University F. S. Noli
11, Rilindasit Blvd., Korçë, 7002, ALBANIA

Abstract

Statistical convergence has become an active area of research under the name of statistical convergence since 1990s of the last century. It has appeared in a wide variety of topics such as number theory, measure theory, trigonometric series, summability theory, in the study of strong integral summability and Banach spaces.

In this paper statistical convergence is used to obtain some new results on amarts. Amarts generalize martingales considerably since every convergent sequence of random variables with integrable supremum is an amart. Our goal is the study of statistical convergence of asymptotic martingales of statistical Bochner integrable functions. We obtain some results for the statistical convergence of vector valued uniform amarts without assuming the Radon-Nikodym Property.

History

Received: 2017-06-14
Revised: 2017-11-15
Published: December 23, 2017

AMS Classification, Key Words

AMS Subject Classification: 60G48, 40A30, 28B05
Key Words and Phrases: statistical convergence, amart, statistical Bochner integrable

Download Section

Download paper from here.
You will need Adobe Acrobat reader. For more information and free download of the reader, see the Adobe Acrobat website.

Bibliography

1

A. Bellow, On vector-valued asymptotic martingales, Proc. Natl. Acad. Sci. USA, 73, No. 6 (1976), 1798-1799

2

A. Bellow, Stability properties of the class of asymptotic martingales, Bulletin of the American Mathematical Society, 82, No. 2 (1976), 338-340

3

A. Caushi, A. Tato, A statistical integral of Bochner type on Banach space, Hikari Ltd Appl. Math. Sci., 6, No. 137-140 (2012), 6857-6870.

4

D. Braho, A. Caushi, On the Statistical Convergence of Martingales, Hikari Ltd Appl. Math. Sci., 9, No. 17(2015), 821- 830.

5

D. Braho, E. Donefski, On the martingale statistical convergence, Aktet, Journal of Institute Alb-Shkenca, 9, No. 1 (2016), 46-49

6

D. Braho, A. Tato, Martingales via statistical convergence, Journal of Advances in Mathematics, 12, No. 7 (2016), 6402-6406.

7

D. Braho, A. Tato, Statistical Convergence of Banach Valued Martingales, ISJ, Journal of Mathematics, 2 (2016), 71-75

8

G. A. Edgar and L. Sucheston, Amarts: A class of asymptotic martingales, A. Discrete parameter, J. Multivariate Anal, 6 (1976), 193-221.

9

H. Çakalli, A study on statistical convergence, Functional analysis, approximation and computation 1:2 (2009), 19-24.

10

I. J. Schoenberg, The integrability of certain functions and related summability methods, The American Mathematical Monthly, 66, No. 5 (1959), 361-375.

11

J. A. Fridy, On statistical convergence. Analysis, 5, No. 4 (1985), 301-313.

12

J. A. Fridy, Statistical limit points. Proceedings of the American Mathematical Society, 118, No. 4 (1993), 1187-1192.

13

J.A. Fridy, C. Orhan, Statistical limit superior and limit inferior, Proc. Amer. Math. Soc., 125, No. 12 (1997), 3625-3631.

14

N. Bouzar, On almost sure convergence without the Radon-Nikodym property, Acta Math. Univ. Comenianae, LXX, No. 2 (2001), 167-175

15

T. Salat, On statistically convergent sequences of real numbers,Math. Slovaca, 30 (1980), 139-150.

16

V. Marraffa, On weakly measurable stochastic processes and absolutely summing operators, 131 Mathematica Bohemica, No. 4 (2006), 379-391

How to Cite?

DOI: 10.12732/ijpam.v117i2.2 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 117
Issue: 2
Pages: 263 - 270

Google Scholar; DOI (International DOI Foundation); WorldCAT.

This work is licensed under the Creative Commons Attribution International License (CC BY).

---