Bounds for Tail Probabilities of Martingales Using Skewness and Kurtosis

@inproceedings{Bentkus2008BoundsFT,
  title={Bounds for Tail Probabilities of Martingales Using Skewness and Kurtosis},
  author={V. Bentkus and Tomas Juskevicius},
  year={2008}
}
Let Mn = X1 + · · ·+ Xn be a sum of independent random variables such that Xk ≤ 1, EXk = 0 and EX2 k = σ2 k for all k. Hoeffding 1963, Theorem 3, proved that P {Mn ≥ nt} ≤ H(t, p), H(t, p) = ( 1 + qt/p )−p−qt( 1− t)qt−q