The Studies Of Inequalities And Strong Law Of Large Numbers For N-Demimartingale

The class of N-demimartingale is introduced in2003by T.C. Christofides, which contains martingale as a special case, and part of sums for negative associated random variables with zero mean is also N-demimartingale. This thesis focuses mainly on inequalities for N-demimartingale, such as Chow type maximal inequality, Doob type maximal inequality, Azuma type inequality, etc. Then prove the strong law of large numbers for N-demimartingale use these inequalities.We mainly research on the inequalities and strong law of large numbers for N-demimartingale in the second chapter. Firstly we discuss the basic properties according to the definition of N-demimartingale and obtain a new result. Then focus on the inequalities for N-demimartingale, which includes the Chow type maximal inequality, Doob type maximal inequality and Azuma type inequality, Marcinkiewicz-Zygmund type inequality for nonnegative N-demimartingale, extend a inequality for N-demisuper-martingale to continuous time parameter N-demisupermartingale, and gain a new inequality, etc. After that we prove the strong law of large numbers for N-demimartingale use these inequalities. Wang X.J. proved a strong law of large numbers for N-demimartingale on condition that p>1in2011, we gain a new strong law of large numbers for N-demimartingale which he has not discussed. Finally, we give a strong law of large numbers for a special form as the application of the strong law of large numbers for N-demimartingale.We further put forward the concept of conditional N-demimartingale on the basis of the work of D.M. Yuan, etal. in the third chapter, and point out the differences and connections between conditional N-demimartingale and N-demimartingale, that is conditional N-demimartingale is a type of N-demimartingale. Then briefly introduce the inequalities and strong law of large numbers for conditional N-demimartingale.