On Hoeffding's Inequality for Dependent Random Variables

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Exponential inequalities for martingales with applications (2013, background): “if E(˘ i 2jF i 1) U i 2 1 ; 1 4 U i 1 + E(˘2jF i 1) U i 1 ; otherwise: (1.19) Then we show that (1.18) implies a generalization of Azuma-Hoeffding’s inequality for martingales due to van de Geer [36]. Moreover, we also show that (1.18) signiﬁcantly improves some recent inequalities of Bentkus [3] ”
Sequential complexities and uniform martingale laws of large numbers (2015, methodology): “For instance, in [34], the quantity supf∈FMn(f) is used to provide bounds on estimation rates for autoregressive models.”
Hoeffding's inequality for sums of weakly dependent random variables (2015, background): “5], Impagliazzo et al. [19], Janson [20], Kallabis et al. [23], Kontorovich et al. [25], Linial et al. [26], McDiarmid [27], Ramon et al. [31], Rio [32], Schmidt et al. [33], Siegel [34], Van de Geer [35], Vu [36], among others. Let us also remark that certain assumptions of ”weak dependence” betwee”