Maximal and moment inequalities for demimartingales and -demimartingales

A note on a law of iterated logarithm for bounded $N$-demimartingales

“…The notion of an N -demimartingale was first introduced by Christofides in [1] as generalization of the concept of negative association which was introduced by Joag-Dev and Proschan in [6]. Over the recent years, various results has been proved.…”

“…Over the recent years, various results has been proved. These results are mainly different kinds of inequalities (see, e.g., [1]- [4], [8], [9]), but also strong laws of large numbers [9], and some results concerning complete convergence of N -demimartingales [4]. D e f i n i t i o n 2.…”

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

“…Hu et al [14] investigated the Marshall type inequalities for demimartingales. Christofides and Hadjikyriakou [15] provided some maximal and moment inequalities for demimartingales, and so forth. For more details about demimartingales, one can refer to [16].…”

“…The concept of demimartingale and demisubmartingale was introduced by Newman and Wright [1] and the notion of N-demimartingale (termed earlier as negative demimartingales in [2]) and N-demisupermartingale was introduced in [2,3].…”

“…Inspired by Agbeko [5], Christofides [3] obtained some maximal inequalities for concave Young functions for Ndemimartingales. Our goal in this paper is to further extend these results to demimartingales and N-demimartingales based on the classes of concave Young functions.…”