Doob's Inequality for Demisubmartingale and the Application of Demisubmartingale's Convergent Theorem

The paper first gives demi-upmartingale's definition and indicates the relationship among demimartingale,demisubmartingale and demi-upmartingale.Then it obtains the Doob's inequality for demisubmartingale using Doob's maximal inequality.It also gives application to demisubmartingale's convergent theorem introduced by Newman and Wright.