On Bernstein-type inequalities for martingales

By K. Dzhaparidze, V. Zanten. 2001

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Estimating discontinuous periodic signals in a time inhomogeneous diffusion (2009, background): “Up to a minor modification which allows for time dependence in the drift, the following result is due to Brandt (2005, Lemma 2.2.4) who extended the classical Bernstein inequality for local martingales (see Formula (1.5) in Dzhaparidze and van Zanten 2001 ) to solutions of SDE.”
Hoeffding’s inequality for supermartingales (2011, methodology): “Further, inequalities for the probabilities P (Xn > x) have been obtained by Prohorov [26], Hoeffding [17], Azuma [1], Steiger [28,29], Freedman [13], Nagaev [21], Haeusler [16], McDiarmid [20], Pinelis [23], Talagrand [30], De La Peña [10], Lesigne and Volný [18], Dzhaparidze and van Zanten [11], N”
Exponential inequalities for martingales with applications (2013, background): “[14] Dzhaparidze, K., and van Zanten, J.H., 2001.”
On the Bennett–Hoeffding inequality (2009, unknown): “Contents Contents 1”
Exponential inequalities for self-normalized martingales with applications (2007, background): “(1.2) Over the last decade, extensive study has been made to establish exponential inequalities for (Mn) relaxing the boundedness assumption on its increments.”