Abstract
In this article, we establish some inequalities associated to a sequence of dyadic martingales. These inequalities are sub-Gaussian type estimates. We derive the inequalities for a regular sequence of dyadic martingales and also for a tail sequence.
Highlights
We first discuss the meaning of the word ‘martingale’
The strategy is that the gambler doubles his bet every time he loses and continues the process, so that the first win would recover all previous losses plus win a profit equal to the original stake
For this let n denote the family of dyadic subintervals of the unit interval [0, 1) of the form
Summary
We first discuss the meaning of the word ‘martingale’. Originally martingale meant a strategy for betting in which you double your bet every time you lose. This process of betting can be represented by a sequence of functions which is an example of dyadic martingale. We give the definition of dyadic martingales. Definition 1.1 (Dyadic Martingale) (Bañuelos and Moore, 1999) A dyadic martingale is a sequence of integrable from [0, 1)
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