Bercu, Bernard et Touati, Abderrahmen, Exponential inequalities for self-normalized martingales with applications, Annals of applied probability , 18(5), 2008, pp. 1848-1869
We propose several exponential inequalities for self-normalized martingales similar to those established by De la Peña. The keystone is the introduction of a new notion of random variable heavy on left or right. Applications associated with linear regressions, autoregressive and branching processes are also provided.