Hoeffding’s inequality for supermartingales

By Xiequan Fan, Ion Grama, Quansheng Liu. 2011

92 citations recorded by the source corpus.

We give an extension of Hoeffding’s inequality to the case of supermartingales with differences bounded from above. Our inequality strengthens or extends the inequalities of Freedman, Bernstein, Prohorov, Bennett and Nagaev.

Subfields: Applied Mathematics, Finance, Management Science and Operations Research

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Finance

In Management Science and Operations Research

Citations in the corpus

Stochastic Primal-Dual Q-Learning (2018, neutral): “To do so, ﬁrst deﬁne and E (2) Then, G T is written by where The next step is to use the Berstein inequality for Martingales (Freedman, 1975; Fan et al., 2012; Bercu et al., 2015) to prove the convergence of G T /T , in (33).”
Time-uniform Chernoff bounds via nonnegative supermartingales (2018, result): “2 in Fan et al. (2015) is based on the inequality ex−x (2)/2 ≤ 1 + x+ x(3)−/3 for all x ∈ R.”
Exponential inequalities for martingales with applications (2013, background): “[16] Fan, X., Grama, I. and Liu, Q., 2012.”
Hoeffding's inequality for sums of weakly dependent random variables (2015, background): “the problem of extending Hoeffding’s theorem to sums of dependent random variables is vast and the interested reader is invited to take a look at the works of Azuma [3], Bentkus[6],Delyon[7],Fanetal. [10],Gavinskyetal. [11],Gradwohletal. [14],Hazla et al. [15], Impagliazzo et al. [19], Janson [20], ”