纯数学证明吗？ 应该不是很简单的说

Notice that Ht is F(t-1) measurable, thus the conditional expectation of E(Zt|F(t-1))=E(Ut/Ht^0.5|F(t-1))=0,thus a m.d.s, which is a special case. I don't know here what do you mean by "strict white noise". If ut means serial uncorrelated, then m.d.s. has implies serial uncorrelated.