Some inequalities for conditional demimartingales and conditional N-demimartingales

In this paper, we establish some maximal inequalities for conditional demi(sub)martingales and minimal inequalities for nonnegative conditional demimartingales. In addition, we get some moment inequalities for conditional N-demimartingales and nonnegative conditional demimartingales by using the conditional Fubini theorem and the conditional Hölder's inequality. As an application, a strong law of large numbers for conditionally associated random variables is obtained.