scholarly journals Statistical convergence of martingale difference sequence via deferred weighted mean and Korovkin-type theorems

2021 ◽  
Vol 22 (1) ◽  
pp. 273
Author(s):  
Bidu Bhusan Jena ◽  
Susanta Kumar Paikray
Keyword(s):  
Statistical Convergence ◽  
Difference Sequence ◽  
Martingale Difference ◽  
Weighted Mean ◽  
Martingale Difference Sequence ◽  
Korovkin Type Theorems

scholarly journals ON THE CENTRAL AND LOCAL LIMIT THEOREM FOR MARTINGALE DIFFERENCE SEQUENCES

2004 ◽  
Vol 04 (02) ◽  
pp. 153-173
Author(s):  
MOHAMED EL MACHKOURI ◽  
DALIBOR VOLNÝ
Keyword(s):  
Limit Theorem ◽  
Local Limit Theorem ◽  
Local Limit ◽  
Ergodic Measure ◽  
Difference Sequence ◽  
Martingale Difference ◽  
Lattice Distribution ◽  
Martingale Difference Sequence ◽  
The Central Limit Theorem ◽  
Difference Sequences

Let [Formula: see text] be a Lebesgue space and T: Ω→Ω an ergodic measure-preserving automorphism with positive entropy. We show that there is a bounded and strictly stationary martingale difference sequence defined on Ω with a common nondegenerate lattice distribution satisfying the central limit theorem with an arbitrarily slow rate of convergence and not satisfying the local limit theorem. A similar result is established for martingale difference sequences with densities provided the entropy is infinite. In addition, the martingale difference sequence may be chosen to be strongly mixing.

scholarly journals A converse to the log-log law for Martingales

1974 ◽  
Vol 17 (4) ◽  
pp. 496-499
Author(s):  
W. L. Steiger
Keyword(s):  
Random Variables ◽  
Difference Sequence ◽  
Martingale Difference ◽  
Martingale Difference Sequence ◽  
Iterated Logarithm ◽  
Present Context ◽  
Log Law ◽  
Independent And Identically Distributed

For sums of independent and identically distributed random variables xn, the HartmanWintner law of the iterated logarithm is equivalent to xn ∈ L2. We show that this is also true when the xn, form a stationary, ergodic martingale difference sequence. This is accomplished by extending a theorem of Volker Strassen to the present context.

Exponential Inequalities for Bounded Random Variables

2015 ◽  
Vol 65 (6) ◽  
Author(s):  
Guangyue Huang ◽  
Xin Guo ◽  
Hongxia Du ◽  
Yi He ◽  
Yu Miao
Keyword(s):  
Markov Chains ◽  
Random Variables ◽  
Independent Random Variables ◽  
Difference Sequence ◽  
Martingale Difference ◽  
Exponential Inequalities ◽  
Martingale Difference Sequence ◽  
Associated Random Variables ◽  
Negatively Associated ◽  
Negatively Associated Random Variables

AbstractIn the paper, several precise exponential inequalities for the sums of bounded or semi-bounded random variables are established, which involve independent random variables, martingale difference sequence, negatively associated random variables, Markov chains.

scholarly journals Operator Fractional Brownian Motion and Martingale Differences

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Hongshuai Dai ◽  
Tien-Chung Hu ◽  
June-Yung Lee
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
The Other ◽  
Difference Sequence ◽  
Martingale Difference ◽  
Martingale Differences ◽  
Martingale Difference Sequence ◽  
Difference Sequences ◽  
Other Hand ◽  
Approximation Sequence

It is well known that martingale difference sequences are very useful in applications and theory. On the other hand, the operator fractional Brownian motion as an extension of the well-known fractional Brownian motion also plays an important role in both applications and theory. In this paper, we study the relation between them. We construct an approximation sequence of operator fractional Brownian motion based on a martingale difference sequence.

scholarly journals Are gold markets weak form efficient? Evidence from China, India and Russia

2018 ◽  
Vol 5 (1) ◽  
pp. 52 ◽  
Author(s):  
Bishart Chang
Keyword(s):  
Random Walks ◽  
Weak Form ◽  
Statistical Techniques ◽  
Special Focus ◽  
Difference Sequence ◽  
Variance Ratio ◽  
Martingale Difference ◽  
Martingale Difference Sequence ◽  
Gold Market ◽  
Non Parametric

The main purpose of this study is to determine the weak form efficiency of the emerging gold markets such as China, India and Russia with the special focus on testing random walks (RWS) and martingale difference sequence (MDS) hypotheses during different periods of time. This study uses biased free statistical techniques such as runs test, parametric variance ratio tests and recent modified non-parametric variance ratio tests based on ranks and signs by using daily spot gold prices from January 12, 1993 to October 28, 2016. Findings of the study suggest that Russian gold market is weak form efficient throughout the period whereas other two markets are found weak form efficient during second sub period only that is, January 2000 to December 2005.

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