The Probability Inequalities For Demi(Sub)- Martingales And Their Applications

The Limit theory of dependent random variable sequence has wide application in applied probability, statistics, insurance and financial mathematics, complex sys-tems, reliability theory, survival analysis and other fields. This thesis focuses mainly on probability inequality for random variable sequence about demi(sub)martingales, such as Chow-type maximal inequality, Doob-type maximal inequality and Minimal inequalities for demisubmartingales. By this inequality, obtained the limit theory.This thesis has some works:(1) Chow’s maximal inequality for demi (sub)martingales is abtained in this pa-per. And Its serves as a "source" inequality for moment inequality of demi(sub)mar-tingales(Doob-type maximal inequality), meanwhile we establish some minimal in-equalities for demi (sub) martingales and nonnegative demimartingales.(2)Then we establish some minimal inequalities for demi(sub)martingales and non-negative demimartingales.