Abstract:

In this article we proved that the occupation time process Y(t) =∫^t₀ X_s ds of the super  process X_t with branching mechanism ψ(z)=z²  and  d≤3  transient Ornstein-Uhlenbeck(O.U.) underlying process, is absolutely continuous with respect to the Lebesgue measure, and its density process Y(t,x) is joint continuous in t≥0,x∈R^d.

Key words: 　ＳｕｐｅｒＯ．Ｕ．ｐｒｏｃｅｓｓ, Ｏｃｃｕｐａｔｉｏｎｔｉｍｅｐｒｏｃｅｓｓ, Ａｂｓｏｌｕｔｅｃｏｎｔｉｎｕｉｔｙ．