Large deviations for martingales.
The authors present new large deviations results for partial sums of martingale differences. Provided boundedness of an exponential moment they prove optimality of the estimate \(\text{e}^{-cn^{1/3}}\) instead of the estimate \(\text{e}^{-cn}\) known for the i.i.d.\ case. Provided boundedness of a \(p\)th moment (\(p\geq 2\)) they show optimality of an estimate \(cn^{-p/2}\) instead of the estimate \(cn^{1-p}\) known for the i.i.d.\ case. Similar results are also derived for a martingale difference field.
scientific article; zbMATH DE number 2138907
scientific article