Some new results for demimartingales

Harremöes obtained some new maximal inequalities for non-negative martingales. In this paper, we get some new maximal and minimal inequalities for non-negative demimartingales which generalize the results of Harremöes. We also obtain an inequality for non-negative demimartingales which generalizes the result of Iksanov and Marynych. Finally we obtain a strong law of large numbers, strong growth rate and integrability of supremum for demimartingales which generalize and improve the result of Chow.