  Much effort has been made to improve the famous step up test of Benjamini and
Hochberg given by linear critical values $\frac{i\alpha}{n}$. It is pointed out
by Gavrilov, Benjamini and Sarkar that step down multiple tests based on the
critical values $\beta_i=\frac{i\alpha}{n+1-i(1-\alpha)}$ still control the
false discovery rate (FDR) at the upper bound $\alpha$ under basic independence
assumptions. Since that result in not longer true for step up tests or
dependent single tests, a big discussion about the corresponding FDR starts in
the literature. The present paper establishes finite sample formulas and bounds
for the FDR and the expected number of false rejections for multiple tests
using critical values $\beta_i$ under martingale and reverse martingale
dependence models. It is pointed out that martingale methods are natural tools
for the treatment of local FDR estimators which are closely connected to the
present coefficients $\beta_i.$ The martingale approach also yields new results
and further inside for the special basic independence model.
