On some maximal inequalities for demimartingales and NN-demimartingales based on concave Young functions

Agbeko (1986) [5] proved some concave function inequalities for sub-(super-) martingales. Christofides (2003) [3] obtained some maximal inequalities for concave Young functions   for NN-demimartingales. In this paper, we will further extend these results to the cases of demimartingales and NN-demimartingales. Our results also generalize and improve partial results of Wang et al. (2010, 2011) [6] and [7].