Maximal and moment inequalities for demimartingales and NN-demimartingales

Newman and Wright (1982) provide an upcrossing inequality for demimartingales while Prakasa Rao (2011) provides a downcrossing inequality for the class of NN-demimartingales. These results are instrumental for obtaining maximal inequalities for demimartingales and NN-demimartingales in this paper. Furthermore, by proving an inequality for nonnegative real numbers we provide moment inequalities for the class of demimartingales.