There is no rebirth / reincarnation (in the sense that the soul takes on a new body after the death of the previous body. )

Our existence is changing process in which there are events like birth and death. In the absence of a unchanging everlasting core the person who is born is not the same as the person who died nor is he a deferent person but but just the continuation of the process of existence. 

In Buddhism what is there is Jati /  birth and death as events in the process keeping us in the cycle of Samsara.

There is no continuity of the person (or some core identity / entity) but there is a continuation of the process.