Abstract
By using some inequalities and properties of martingale differences, we investigate the moment of maximum normed randomly weighted sums of martingale differences under some weakly conditions. A sufficient condition to the moment of this stochastic sequence with maximum norm is presented in this paper.
Highlights
Let {Xn, n ≥ } be a sequence, independent and identically distributed with EX =
By using the method of dominated by a nonnegative random variable, we investigate the randomly weighted sums of martingale differences under some weakly conditions
A bound on tail probabilities for quadratic forms in independent random variables is seen by using the following condition
Summary
) are equivalent under the dependent case such as ρ-mixing random variables. By using the method of dominated by a nonnegative random variable, we investigate the randomly weighted sums of martingale differences under some weakly conditions. We generalize the result of Chen and Gan [ ] for ρ-mixing random variables to the case of randomly weighted sums of martingale differences.
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